Algebra and Trigonometry (4th Edition)

Chapter 10

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coordinate ; Rectangular and polar coordinates are... more

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Yes. ; Convert to its equivalent rectangular ... more

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No. A point with rectangular coordinates can be ... more

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The given point is in the form . Locate .The ... more

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The given point is in the form . Locate by moving... more

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The given point is in the form . Locate .The ... more

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The given point is in the form . Locate .The ... more

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The given point is in the form . Locate .The ... more

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The given point is in the form . Locate .Find an ... more

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; The given point is in the form . Locate .The ... more

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; The given point is in the form . Locate .The ... more

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; The given point is in the form . Locate .The ... more

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; The given point is in the form . Locate .The ... more

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; The given point is in the form . Locate . Move ... more

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; The given point is in the form . Locate .A ... more

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; Locate .The radian measure is equivalent to .... more

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; Locate .The radian measure is equivalent to .... more

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; Locate .The radian measure is equivalent to .... more

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; Locate .Find a positive angle coterminal with ... more

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; Locate .Find a positive angle coterminal with ... more

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; Locate .Find a positive angle coterminal with ... more

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; Locate .Find a positive angle coterminal with ... more

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; Locate .Find a positive angle coterminal with ... more

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; The given point is in quadrant II with and . ... more

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; The given point is on the negative -axis with ... more

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; It is given that and . Find the - coordinate ... more

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; It is given that and . Find the - coordinate ... more

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; It is given that and . Find the - coordinate ... more

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; Compare the given point with and write the ... more

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; Compare the given point with and write the ... more

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; Compare the given polar coordinates to the ... more

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; Compare the given polar coordinates with the ... more

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; Compare the given polar coordinates with the ... more

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; Compare the given polar coordinates to the ... more

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; Compare the given polar coordinates to the ... more

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; Given the rectangular coordinates , the value ... more

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; Given the rectangular coordinates , the value ... more

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; Given the rectangular coordinates , the value ... more

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; Given the rectangular coordinates , the value ... more

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; Given the rectangular coordinates , the value ... more

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; Given the rectangular coordinates , the value ... more

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; Given the rectangular coordinates , the value ... more

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; Substitute and in the given equation. ; ... more

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; Substitute and in the given equation. ; Use ... more

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; Substitute and   in the given equation. ; ... more

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; Substitute in the given equation. ; Apply the ... more

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; Substitute in the given equation. ; Apply the ... more

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; There are no other parameters, just a radius, ... more

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; Use the equation and then substitute for... more

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; Substitute for in and . ; Since, and value ... more

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; Substitute the value of to find and where ... more

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; Substitute for in the given equation.  ; more

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; Given the equation , substitute . ; Since , ... more

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; Given the equation , the variable can be ... more

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; Multiply on both sides of the given equation... more

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; Multiply both sides of the given equation by... more

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; Multiply both sides of the given equation by... more

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; Multiply both sides by . ; Substitute and . ; ... more

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; Multiply both sides by . ; Substitute and . ; ... more

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; Multiply both sides by . ;   ; Substitute and... more

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; Multiply both sides by . ; Substitute .  ; ... more

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; Multiply both sides by . ; Substitute . ; ... more

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; Multiply both sides by . ; Substitute . ; ... more

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; Substitute . ; Substitute . ; more

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; Apply the double angle formula to expand . ; ... more

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; Express in terms of . ; Since , . ; Square on ... more

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; Apply the double angle formula for . ; Since... more

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circles ; The polar graph consists of concentric ... more

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Please refer to the illustration above in graphing... more

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Symmetric about the line ; Check for symmetry ... more

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Symmetric about the polar axis ; Check for ... more

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Symmetric about the polar axis ; Check for ... more

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Symmetric about the pole ; Check for symmetry ... more

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Symmetric about the line ; Check for symmetry ... more

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Symmetric about the polar axis ; Check for ... more

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Symmetric about the polar axis, pole and the line... more

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Symmetric about the pole and the line ; Check for ... more

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; The equation represents the points which are 2... more

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; The equation represents the points which are 1... more

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; The equation represents all the points which ... more

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; The equation represents all the points which ... more

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Note that in the graph. ; Graph the given ... more

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Note that in the graph. ; Graph the given ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Find the values of for which . ; Find the value ... more

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Graph the given equation in rectangular ... more

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Find the value of at . ; Graph the given equation... more

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Find the values of for which . ; Graph the given ... more

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Find the values of for which . ; Find the value ... more

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Find the values of for which . ; Graph the given ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Graph the given equation in rectangular ... more

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Solve the given equation for by dividing both ... more

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Solve the equation for . ; Graph the given ... more

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Graph the given equation in rectangular ... more

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Find the domain to graph the complete curve:The ... more

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Find the domain to graph the complete curve:The ... more

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Find the domain to graph the complete curve:The ... more

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Find the domain to graph the complete curve:The ... more

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There are loops in the graph of the equation . ; ... more

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When , the dimples in the loop becomes deeper.When... more

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IV ; Find the maximum value of . Substitute for ... more

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I ; Based on the given equation, it can be ... more

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III ; Since becomes 0 for , the value of is ... more

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II ; Find the value of at . So, at . The graph ... more

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Convert the given equation to polar coordinates.... more

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Convert the given equation to polar coordinates.... more

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Convert the given equation to polar coordinates:... more

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Convert the given equation to polar coordinates:... more

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The graph of is obtained by rotating the graph of... more

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The equations of the circle and four-leaved rose ... more

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Simpler in the rectangular coordinate systemChoose... more

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real ; In the given complex number, the term which... more

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422 ; The number of roots of a complex number is... more

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4 ; Graph the complex number. Locate on the ... more

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3 ; Graph the complex number. Locate on the ... more

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2 ; Graph the complex number. Locate on the ... more

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6 ; Graph the complex number. Locate 6 on the ... more

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; Graph the complex number. Locate 5 on the ... more

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; Graph the complex number. Locate 7 on the ... more

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2 ; Graph the complex number. Locate on the ... more

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; Graph the complex number. Locate on the ... more

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1 ; Rewrite the given complex number as a sum of ... more

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1 ; Rewrite the given complex number as a sum of ... more

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Evaluate , and . ; Locate the evaluated complex ... more

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Evaluate , and . ; Locate the evaluated complex ... more

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Find the complex conjugate of . ; Locate and on ... more

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Find the complex conjugate of . ; Locate and on ... more

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Evaluate . ; Evaluate . ; Locate , , and . ; more

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Evaluate . ; Evaluate . ; Locate , , and . ; more

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The real part means that the values of lie on ... more

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The real part means that the values of lie on ... more

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The set includes all the points which are at a ... more

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Since , the distance of the point corresponding to... more

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Since , the distance of the point corresponding to... more

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The given set includes the complex numbers whose ... more

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Draw a line given by the equation . Since , the ... more

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Since , the complex numbers lying on the line and... more

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; Find the modulus .  ; Find the argument . ; ... more

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; Graph the given complex number. ; Compare with... more

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; Graph the given complex number. ; Compare with... more

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; Graph the given complex number. ; Compare with... more

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; Graph the given complex number. ; Compare with... more

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; Graph the given complex number.  ; Compare ... more

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; Graph the given complex number. ; Compare with... more

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; Graph the given complex number. ; Compare with... more

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; Graph the given complex number. ; Compare with... more

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; Graph the given complex number. ; Compare with... more

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; Graph the given complex number. ; Compare with... more

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  ; Graph the given complex number. ; Compare ... more

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; Graph the given complex number. ; Compare with... more

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; Graph the given complex number. ; Compare with... more

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; Graph the complex number. ; Compare with and ... more

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; Graph the complex number. ; Compare with and ... more

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; Apply the distributive property and distribute ... more

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; Distribute inside the bracket.Substitute to ... more

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; Distribute inside the bracket. ; Graph the ... more

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; Distribute inside the bracketSubstitute to ... more

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; Substitute the values and in and simplify... more

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; Substitute the values and in and simplify... more

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; Substitute the values and in and simplify... more

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; Substitute the values and in and simplify... more

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; Substitute the values and in and simplify... more

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; Substitute the values and in and simplify... more

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; Substitute the values and in and simplify... more

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; Substitute the values and in and simplify... more

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; Perform the following steps to get the polar ... more

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; Perform the following steps to get the polar ... more

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; Perform the following steps to get the polar ... more

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; Perform the following steps to get the polar ... more

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; Perform the following steps to get the polar ... more

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; Perform the following steps to get the polar ... more

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; Perform the following steps to get the polar ... more

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; Perform the following steps to get the polar ... more

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; Find the polar form of by using the following ... more

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; Find the polar form of by using the following ... more

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; Find the polar form of by using the following ... more

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; Find the polar form of by using the following ... more

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; Find the polar form of by using the following ... more

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; Find the polar form of by using the following ... more

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4096 ; Find the polar form of by using the ... more

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1 ; Find the polar form of by using the following... more

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; Find the polar form of by using the following ... more

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; Find the polar form of by using the following ... more

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; Find the polar form of by using the following ... more

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; Find the polar form of by using the following ... more

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; Find the polar form of by using the following ... more

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; Find the polar form of by using the following ... more

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; Find the polar form of by using the following ... more

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2 ; Graph the complex number on the complex plane ... more

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; Graph the complex number on the complex plane ... more

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; Use the formula to find the modulus in the ... more

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; Graph the complex number on the complex plane ... more

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; Graph the complex number on the complex plane ... more

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; Graph the complex number on the complex plane ... more

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; Use the formula to find the modulus in the ... more

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; Subtracting 1 from both sides, the equation ... more

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; Adding to both sides, the equation becomes . ... more

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; Adding to both sides, the equation becomes . ... more

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; Adding 1 to both sides, the equation becomes . ... more

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; Subtracting 1 from both sides, the equation ... more

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1 ; Adding 1 to both sides, the equation becomes... more

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; Use the quadratic formula to solve for .The ... more

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; Use the quadratic formula to solve for . ... more

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; Use the quadratic formula to solve for . ... more

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; Use the quadratic formula to solve for . ... more

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In polar form, can be written as . Using the ... more

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Since is an root of , it follows that . Also, that... more

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The cube roots of 1 are 1 and , which add up to 0... more

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The product of the cube roots of 1 is 1. ; The ... more

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3Counterclockwise sec ; Find the radius. Square ... more

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2Clockwise sec ; Find the radius.Square both ... more

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1Clockwise sec ; Find the radius.Square both ... more

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4Counterclockwise sec ; Find the radius: Square ... more

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, ; Since the slope of the line is , for increment... more

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, ; Since the slope of the line is , for increment... more

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, ; From the point to , the increment in -... more

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, ; From the origin to , the increment in -... more

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, ; Divide both sides of the equation of the ... more

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, ; Substitute for and   for .The resulting ... more

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The given parametric equation can be written as . ... more

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Adjust the window setting. Be sure to change the ... more

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Adjust the window setting. Be sure to change the ... more

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Adjust the window setting. Be sure to change the ... more

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Adjust the window setting. Be sure to change the ... more

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Adjust the window setting. Be sure to change the ... more

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Adjust the window setting. Be sure to change the ... more

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As , and . Meanwhile, as , and . ; When and , and... more

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; Solve for and . ; Substitute the equivalent ... more

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Substituting the parametric equations , into the ... more

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Find the values of and for different values of .... more

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Find the values of and for different values of .... more

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Find the values of and for different values of .... more

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Find the values of and for different values of ... more

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; Draw and label the diagram as follows. Find the... more

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; Find the and coordinates of .A circle with ... more

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; Solve for in .Distribute .Subtract from both ... more

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Find the domain of :The value of is the same at ... more

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Find the domain of :The value of is the same at ... more

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Find the domain of :The value of is the same at ... more

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Graph the polar equation using a graphing utility:... more

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; Compare with .  ; Substitute and into to ... more

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16 ; Compare with .  ; Substitute and into to ... more

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; Compare with .  ; Substitute and into to ... more

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; Compare with .  ; Substitute and into to ... more

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; Compare with .  ; Substitute and into to ... more

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; Compare with .  ; Substitute and into to ... more

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; Compare 1 with .  ; Substitute and into to ... more

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; Compare with .  ; Substitute and into to ... more

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Find the period:The period of and is given as . ... more

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The range of sine and cosine trigonometric ... more

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  ; Redraw the figure and label them.  ; Use the ... more

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Limacons ; Sketch the graph of in the rectangular ... more

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; Use multiplication formula of complex numbers... more

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; Compare with .  ; Substitute and into to ... more

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; Let be a starting point. Since the line has a ... more

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Solve for and substitute into .The resulting ... more

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Use the parametric equation of projectile motion .... more

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  ; Write the general parametric equations for the... more

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No, the greatest firing range is not attained at... more

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