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Chapter 9: Q 47. (page 731)

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.

r=sin3胃

Short Answer

Expert verified

The required equation isx2+y22=y3.

Step by step solution

01

Step 1. Given information.

The given equation in polar coordinates is:

r=sin3胃

02

Step 2. Find the equation in rectangular coordinates. 

r=sin3胃r=yr3yr=sin胃r=yr33

Now cross multiply,

role="math" localid="1649325945189" r4=y3x2+y24=y3r2=x2+y2andr=x2+y2x2+y242=y3x2+y22=y3

Therefore, the equation in rectangular coordinates isx2+y22=y3.

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Most popular questions from this chapter

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.

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In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral

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Consider the hyperbola with equation x2A2-y2B2=1.Let F be the focus with coordinates (A2+B2,0).Let e=A2+B2A and l be the vertical line with equation x=Ae. Show that for any point P on the hyperbola, FPDP=e,where D is the point on l closest to P.

In Exercises 48鈥�55 convert the equations given in rectangular coordinates to equations in polar coordinates.

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In exercise 26-30 Find a definite integral that represents the length of the specified polar curve and then find the exact value of integral

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