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Chapter 9: Q. 47 (page 747)

Graph the cardioidsr=1+sin胃andr=1鈭�sin胃. What is the relationship between these two graphs?

Short Answer

Expert verified

Both the graphs intersect each other at certain points.

Step by step solution

01

Step 1. Given Information.

The given curves are r=1+sin胃andr=1鈭�sin胃.

02

Step 2. Graphically

The equations will be as :

r=1+asin胃

Both the graph intersect each other at certain points. Changing the value of achanges the size of the cardioid but does not affect its shape. The larger the value of a, the larger the resulting cardioid.

The graphs of a given curve are :

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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.

0,-3

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

directrixx=3, focus(0,1)

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

y=3x

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

r=伪1+cos胃

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

The entire limacon r=1+2sin胃
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