Algebra & Trigonometry (10th Edition)

Chapter 7

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; It is given that the central angle is . The ... more

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. ; The total arc length covered by the second ... more

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; It is given that the sprinkler rotates through ... more

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Trigonometry is a branch of mathematics that ... more

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An angle is determined by rotating a ray (half-... more

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Coterminal. ; When two angles have the same ... more

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Degree. ; The degree is a measure of an angle. It ... more

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Complementary. ; Any two positive angles are ... more

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Radian. ; The measure of an angle determines the ... more

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Concept-  Angular speed measures how fast the ... more

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; The region bounded by two radii and its ... more

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; The angle is in the anticlockwise direction; ... more

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; The angle is in the anticlockwise direction and... more

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; The angle is in the clockwise direction and, ... more

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; The angle is in the clockwise direction and, ... more

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; On estimation, it is found that the angle could... more

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-3 ; The angle lies in the negative direction, and... more

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; On estimation, it is found that the acute angle... more

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6.5 ; The angle lies in the positive direction, ... more

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. ; To convert the angle from degree to radian, ... more

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Hope it will be helpful to youPlease ask below the... more

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Approximately ; To convert the angle from radians... more

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Approximately ; To convert the angle from radians... more

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; The length of a circular arc from a circle of ... more

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Here is the step by step explanation.   more

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; The central angle of a circle of radius that ... more

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; The central angle of a circle of radius that ... more

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Given:-Radius, r=700 mArc length, s=3.5 km=3.5×... more

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Approximately ; For a circle with radius and ... more

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Approximately ; Convert from degrees into radians... more

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There is an error in the conversion of degrees ... more

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There is an error in the angle The angle used in ... more

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Approximately ; Find the difference between the ... more

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Approximately ; Find the difference between the ... more

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Approximately ; Substitute 2.5 for and 6 for in... more

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; Let the total length of the wiper be , the ... more

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Approximately, . ; The area of the sector of the ... more

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The problem can be viewed as a circle problem. The... more

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False; is in the degree measure. ; Both the ... more

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False; Two complete revolutions equal to ; One ... more

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True;As one revolution corresponds to or , the ... more

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False;  The angle lies on the -axis. ; The angle... more

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When is constant, the length of the intercepted ... more

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B and C are coterminal angles for angle A because ... more

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The speed increases when the radius increases ... more

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A radian; is approximately . ; Since, the full ... more

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Consider a circular sector that is like a triangle... more

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;;;;; ; Given and .According to the Pythagoras ... more

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; Given ,, and .Apply the formulas for the ... more

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; To compute , given , , and .Calculate by the ... more

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Approximately ; In the triangle , define the ... more

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; From the definition of cosine, it can be ... more

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Approximately ;Approximately ; To calculate , use ... more

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Sine of any angle is defined in a right-angled ... more

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Hypotenuse. ; The side that meets the opposite ... more

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Complementary. ; For a right-angled triangle and... more

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Elevation. ; The angle of elevation is the angle ... more

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; The length of the side opposite to , is 6.The ... more

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; The length of the side opposite, , is 5.The ... more

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; The length of the side opposite to , is 9.The ... more

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; The length of the side adjacent to , is 7.The ... more

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; The length of the side opposite to , is 4.The ... more

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; The length of the side opposite to , is 7.The ... more

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Both triangles are similar, and hence, the ... more

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Both triangles are similar, and hence, the ... more

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Both triangles are similar, and hence, the ... more

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Both triangles are similar, and hence, the ... more

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;; ;; ; By comparing the value of with , it can ... more

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; ; ;; ; By comparing the value of with , it can ... more

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; On comparing the given trigonometric function ... more

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; ; ; ;;  ; On comparing the given trigonometric ... more

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; ; ; ;; ; On comparing the given trigonometric ... more

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; ; ; ; ; ; On comparing the given trigonometric ... more

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; ; ; ; ; ; On comparing the given trigonometric ... more

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; ;;;; ; On comparing the given trigonometric ... more

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; ; To convert the angle from degrees into radian... more

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; ; To convert the angle from degrees into radian... more

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; ; To convert the angle from radians into degree... more

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; ; To convert the angle from radians into degree... more

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, ; To convert the angle from radians into degree... more

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; 2 ; To convert the angle from radians into ... more

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Start by substituting on the left-hand side of ... more

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Apply the formula in the left side of the given ... more

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Apply the formula in the left side of the given ... more

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Apply the formula in the left side of the given ... more

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Apply the formula in the left side of the given ... more

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Apply the formula in the left side of the given ... more

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Apply the formula in the left side of the given ... more

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Apply the property in the left side of the given ... more

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; Let us begin the calculation from the left-side... more

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; Let us begin the calculation from the left-side... more

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; It can be observed that for , , , and . To find... more

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; It can be observed that for , , , and . To find... more

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; It can be observed that for , , , and . To find... more

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; It can be observed that for , , , and . To find... more

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Approximate height of the building: Distance ... more

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; The height of the mountain is and the angle of... more

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; The tangent of an angle in a right-angled ... more

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or . ; The tangent of an angle in a right-angled ... more

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. ; The abscissa can be represented in terms of ... more

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; The tapered shaft is the frustum of a cone with... more

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; ; Use a ruler to measure the abscissa and the ... more

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There should be the adjacent side of the triangle ... more

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The sine of an angle in a right-angled triangle is... more

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False.Values of the secant and cosecant functions ... more

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False.The sum of the sine and cosine values is not... more

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True.Values of the sine and cosine functions are ... more

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False.Values of the fraction is not equal to . ; ... more

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False.The value of the right side of the given ... more

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YesSecant function is the fraction of the ... more

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... ; Since the point is on the terminal side of... more

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.. ; Apply the formula to find the value of ... more

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.. ; The angle is the sum of and .Apply the sine... more

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Reference. ; The reference angle is the standard ... more

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thank you.....please upvote more

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; The point on the terminal side of the angle is... more

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; The point on the terminal side of the angle is... more

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; The point on the terminal side of the angle is... more

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; The point on the terminal side of the angle is... more

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; The point on the terminal side of the angle is... more

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; The point on the terminal side of the angle is... more

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Quadrant 1 ; The value of and .Both sine and ... more

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Quadrant 3 ; The value of and .Both sine and ... more

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Quadrant 2 ; The value of and .The value of sine ... more

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Quadrant 4 ; The value of and .The value of ... more

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; The value of and .Therefore, .Since the values... more

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; The value of and .Therefore, .Since the value ... more

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; The value of , and lies in Quadrant 2.... more

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; The value of , and lies in Quadrant 3.... more

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; The value of and .Therefore, .The value of is... more

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; The value of and .Therefore, .The value of is... more

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. ; Find the reciprocal of the given cosine and ... more

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. ; Find the reciprocal of the sine function and ... more

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is undefined.. ; It is given that is undefined.... more

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is undefined.. ; Given: is undefined Since , ... more

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. ; Sine and cosecant functions in the second ... more

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. ; It is given that , which is in the third ... more

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. ; It is given that ; it implies that , which is ... more

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. ; It is given that ; it implies that , which is ... more

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0. ; Find the value of the sine function at the ... more

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-1. ; Write as the sum of and .Use the cosecant ... more

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Undefined. ; Write as the sum of and .Use the ... more

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-1. ; Secant function is the reciprocal of the ... more

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1. ; Find the value of the sine function for the ... more

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Undefined. ; Cotangent function is the reciprocal ... more

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Undefined. ; Cosecant function is the reciprocal ... more

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0. ; Cotangent function is the reciprocal of the ... more

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0. ; Write as the sum of and .Apply the cosine ... more

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Undefined. ; Apply the value of tangent function ... more

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. ; Since lies in the second quadrant.Hence, ... more

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. ; Since lies in the fourth quadrant.Hence, ... more

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. ; The angle lies in the third quadrant; it ... more

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. ; The angle lies in the second quadrant; it ... more

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. ; The angle lies in the second quadrant.Hence, ... more

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. ; The angle lies in the third quadrant.Hence, ... more

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. ; The given angle is in radians.Hence, multiply... more

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. ; The given angle measures in radians.Hence, ... more

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. ; The angle lies in the third quadrant, hence ... more

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. ; The angle lies in the fourth quadrant, hence ... more

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. ; The angle lies in the first quadrant and is ... more

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. ; The angle lies in the fourth quadrant and ... more

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. ; The angle lies in the third quadrant, which ... more

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. ; The angle lies in the second quadrant and ... more

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... ; The angle lies in the second quadrant and ... more

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. ; Write as , and apply the trigonometric ... more

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. ; Find the value of the sine function for the ... more

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. ; Write as , and apply the trigonometric ... more

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. ; Write as , and apply the trigonometric ... more

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. ; Write as , and apply the trigonometric ... more

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. ; Write as , and apply the trigonometric ... more

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. ; The given angle can also be written as , ... more

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. ; Apply the trigonometric identity to find the ... more

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. ; Apply the trigonometric identity to find the ... more

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. ; Apply the trigonometric identity to find the ... more

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. ; Apply the trigonometric identity to find the ... more

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. ; Apply the trigonometric identity to find the ... more

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. ; Apply the trigonometric identity to find the ... more

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0.1736. ; Use calculator to find the sine function... more

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-1.4826. ; Use a calculator to find the tangent ... more

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-0.3420. ; Use a calculator to find the cosine ... more

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-0.5. ; Use a calculator to find the sine function... more

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-28.6363. ; Use a calculator to find the cotangent... more

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3.2361 ; Use calculator to find the secant ... more

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1.4142 ; Use calculator to find the cosecant ... more

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-2.7475 ; Use calculator to find the cotangent ... more

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0.3640 ; Use the calculator to find the tangent ... more

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0.6235. ; Use a calculator to find the cosine ... more

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-2.6131. ; Use a calculator to find the secant ... more

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-1.4142. ; Use a calculator to find the cosecant ... more

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-0.6052. ; Use a calculator to find the sine ... more

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0.2190. ; Use a calculator to find the cosine ... more

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1.8382 ; Select the Radian mode in the calculator.... more

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-8.9164 ; Select the Radian mode in the calculator... more

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Refer to the unit circle given below,From the unit... more

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Refer to the unit circle below,The x coordinate of... more

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. ; Substitute by 0.7 in the given equation to ... more

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False.The sign of the secant function is negative ... more

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False.The reference angle of the angle in the ... more

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decreases from 12 to 0. increases from 0 to 12.... more

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; The reference angle is the positive acute angle... more

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The amplitude of is 2. Therefore, the maximum ... more

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The amplitude is 1 in this case and . Accordingly... more

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The amplitude of the graph is 2 and period is ... more

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Determine the left end point of a one cycle ... more

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For the given expression, the amplitude is 2 and ... more

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; Amplitude is half of the difference between the... more

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Cycle. ; After completing one cycle, the graph ... more

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Amplitude. ; As the amplitude is the height from ... more

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Phase shift. ; The graph of is shifted to . The ... more

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Vertical shift. ; Adding to the input values ... more

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Period: Amplitude: 2  ; Compare by . Then, and... more

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Period:  Amplitude: 3 ; Compare by . Then, and... more

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Period: 4Amplitude: ; Compare by . Then, and .... more

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; Compare by . Then, and .Period, , is given as ... more

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; Compare by . Then and .Period is given as ... more

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Period: Amplitude: ; Compare the given equation ... more

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Period: 24Amplitude: ; Compare the given equation ... more

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Period: Amplitude: ; Compare the given equation ... more

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The period of is one-fifth of the period of . ; ... more

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The amplitude of is twice the period of . ; The ... more

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The graph of is the graph of reflected along the... more

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The graph of is the graph of reflected along the... more

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is a horizontal shift of by units to the right... more

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is a horizontal shift of by units to the left... more

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is a vertical shift of by three units in the ... more

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is a vertical shift of by two units in the ... more

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The amplitude of is twice the amplitude of . ; ... more

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The period of is thrice the period of . ; Both ... more

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is a horizontal shift of by units to the right... more

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is a vertical shift of by two units in the upward... more

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For a trigonometric function , the period is , the... more

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For a trigonometric function , the period is , the... more

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For a trigonometric function , the period is , the... more

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For a trigonometric function , the period is , the... more

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For a trigonometric function , the period is , the... more

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For a trigonometric function , the period is , ... more

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Period is a complete oscillation of the graph. The... more

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Period is a complete oscillation of the graph. The... more

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Period is a complete oscillation of the graph. The... more

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Period is a complete oscillation of the graph. The... more

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The period of the function or is determined by... more

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The period of the function or is determined by... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete cycle of the graph. The ... more

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A period is a complete cycle of the graph. The ... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete cycle of the graph. The ... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete oscillation of the graph. ... more

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A period is a complete oscillation of the graph. ... more

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Input the function in the graphing utility. Use ... more

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Input the function in the graphing utility. Use ... more

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Input the function in the graphing utility. Use ... more

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Input the function in the graphing utility. Use ... more

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Input the function in the graphing utility. Use ... more

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Input the function in the graphing utility. Use ... more

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, ; For the function , let the maximum value of ... more

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, ; For the function , let the maximum value of ... more

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, ; For the function , let the maximum value of ... more

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, ; For the function , let the maximum value of ... more

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 , , ; For the function , let the maximum value ... more

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 , , ; For the function , let the maximum value ... more

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 , , ; For the function , let the maximum value of... more

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 , ,   ; For the function , let the maximum value ... more

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; Enter the function and in the graphing ... more

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; Enter the function and in the graphing ... more

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; Amplitude .Period is given by . Substitute for... more

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; Amplitude .Period is given by . Substitute for... more

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; Amplitude .Period is given by . Substitute for... more

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; Amplitude .Period is given by . Substitute for... more

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False. The graph of shift 1 period in the left ... more

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False. The amplitude of is twice the amplitude of... more

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True, as . ; The transformation made by ... more

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The graphs of both the functions coincide. ; For ... more

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The graphs of both the functions coincide. ; For ... more

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The graphs converge as the value of increases.0 ... more

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Calculate the vertical asymptotes of the function... more

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Calculate the vertical asymptotes of the function... more

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The value of for different values of is ... more

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Given function: Plot the graph of (the gray curve... more

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Given function: Plot the graph of (the gray curve... more

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Given function: Break this into two functions:  ... more

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Odd; origin ; The odd functions are those for ... more

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Vertical ; When the and functions are 0, the... more

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Reciprocal ; To draw the graphs of and , first ... more

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Damping ; For any function of the form , is ... more

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; is not defined for all the integral values of... more

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; The range of is (-1,1). So, the range of will... more

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; The range of is (-1,1). So, the range of will... more

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It can be seen that the period is . ; It can be ... more

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function is tan(2x​) first, we know how tan(x) ... more

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the secant function sec x is the inverse of cos x... more

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The value of for different values of is ... more

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The value of  for different values of is ... more

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Given function: Plot the graph of (the gray curve... more

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Given function: Plot the graph of (the gray curve... more

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The value of for different values of is ... more

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The value of for different values of is ... more

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Given function: Plot the graph of (the gray curve... more

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The function plotted in the above graph is .The ... more

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From the graph, it is observed that the given ... more

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The function plotted in the above graph is . The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is . The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The function plotted in the above graph is .The ... more

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The period of the given function is and the ... more

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The period of the given function is and the phase... more

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The period of the given function is and it has a ... more

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To graph the given function, follow the given ... more

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To graph the given function, follow the steps ... more

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To graph the given function, follow the given ... more

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To graph the given function, follow the given ... more

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; The values of for which the tangent function ... more

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; The values of which will satisfy the given ... more

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; The values of for which the given equation ... more

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; The values of which satisfy the given equation... more

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; The values of which satisfy the given equation... more

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From the graph, it can be observed that the two ... more

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From the graph, it can be observed that the two ... more

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From the graph, it can be observed that the two ... more

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Even ; Plot the graph of , denoted by the gray ... more

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As , , the range of absolute value functions is ... more

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Here the given function is g(x)=∣x∣cosx... more

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The functions are equal. ; To plot the graph of , ... more

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The functions are equal. ; To plot the function , ... more

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The functions are equal. ; The period of the given... more

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The functions are equal. ; The period of the given... more

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As , ; Consider as the product of two functions ... more

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As , ; Consider as a product of two functions and... more

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As ; Consider as a product of two functions and  ... more

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As ; Consider as a product of two functions and . ... more

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As , ; To graph the functions, follow the given ... more

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As , ; To graph the functions, follow the given ... more

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As , ; To graph the functions, follow the given ... more

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As ; To graph the functions, follow the given ... more

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As oscillates between -1 and 1. ; To graph the ... more

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As , oscillates between and . ; To graph the ... more

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; Evaluate the distance function in the form of ... more

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; Evaluate the distance function in the form of ... more

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True, the coordinate for the function is equal ... more

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True, the reciprocal of is horizontally ... more

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The graph of is a reflection of the graph of ... more

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; It is known that the value of is -1. Applying ... more

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; Let , then, . As, the range of inverse tangent ... more

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; As the hypotenuse is given as the sum of ... more

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; The arcsine function is the inverse of the sine... more

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; An inverse cosine function can be denoted by ... more

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; An inverse tangent function can be denoted by ... more

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Inverse. ; In frequently occurring cases, there is... more

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; It is known that and lies in the range . ... more

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0 ; It is known that and 0 lie in the range .So... more

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. ; It is known that and lie in the range . ... more

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; It is known that and lies in the range . ... more

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; It is known that and lies in the range . ... more

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; It is known that and lies in the range . ... more

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No possible solution. ; The domain of an inverse ... more

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; It is known that and lie in the range . ... more

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; It is known that and lie in the range . ... more

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No possible solution. ; The domain of the inverse ... more

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; It is known that and lies in the range . ... more

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; It is known that and lie in the range . ... more

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; It is known that and lie in the range . ... more

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