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Chapter 9: Q. 10. (page 755)

Explain how to use parametric equations to transform a

polar function r=f(胃)

Short Answer

Expert verified

The parametric equations arex=(1-sin胃)cos胃,y=(1-sin胃)sin胃

Step by step solution

01

Given information 

The polar function isr=f(胃)

02

The objective is to transform the polar equation of the form r=f(θ)  into the parametric equations.

The function r=f(胃)is simply expressed using parametric equations of the form x=x(胃),y=y(胃)where 胃is the parameter.

To convert polar coordinates into rectangle coordinatesx=rcos胃,y=rsin胃

03

 write the parametric equations for r=1-sinθ 

If r=f(胃)then,

x=f(胃)cos胃,y=f(胃)sin胃.

The parametric equations for r=1-sin胃

The parametric equations have the following form:

x=f(胃)cos胃,y=f(胃)sin胃

Then the parametric equations are:

x=(1-sin胃)cos胃,y=(1-sin胃)sin胃

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Most popular questions from this chapter

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

the spiralr=e胃for0鈮�胃鈮�2蟺

In exercises 31-36 find a definite integral that represents the length of the specified polar curve, and then use a graphing calculator or computer algebra system to approximate the value of integral

Onepetalofthepolarroser=cos2胃

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

胃=蟺

Each of the integral in exercise 38-44 represents the area of a region in a plane use polar coordinates to sketch the region and evaluate the expression

The integral isA=鈭�0蟺2sin2胃d胃

Sketch the graphs of the equations

r=22+cos胃and localid="1649860998050" r=22+sin胃

What is the relationship between these graphs? What is the eccentricity of each graph?
See all solutions

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