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Chapter 9: Q. 9. (page 755)

Explain how the symmetries of the graphs of polar functions

can be used to simplify area calculations

Short Answer

Expert verified

To circumvent this problem, we calculate a portion of the entire area and multiply it by the number of other sections.

To put it another way, choose a known fraction of the total area and multiply it by the relevant factor.

Step by step solution

01

Given information

Given statement is: the symmetries of the graphs of polar function can be used to simplify area calculations

02

We use the symmetry of the curves to calculate the area of some curves.

If a curve is symmetric, one component of it is positive and the other is negative. To avoid this problem, we calculate one part of the total area and multiply it by the number of other parts.

To put it another way, choose a known fraction of total area and multiply it by the relevant factor.

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Most popular questions from this chapter

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

x=4

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

directrixx=x0, focusx1,y1,wherex0≠x1.

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
r=6cscθ

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

r=31+cosθ

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

r=sin2θ
See all solutions

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