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Chapter 9: Q. 21 (page 747)

Graph the equation in the 胃r-plane. Label each arc of your curve with the quadrant in which the corresponding polar graph will occur.

r=cos2胃

Short Answer

Expert verified

The graph of the equation:

Step by step solution

01

Step 1. Given information

The equation of the curve:

r=cos2胃

02

Step 2. Simplify the equation:

The function can be simplified as:

r=cos2胃r=1+cos2胃2r=12+12cos2胃

03

Step 3. Graph the equation in θr-plane. 

The value of 胃lies on the horizontal axis and rlies on the vertical axis.

The graph of r=12+12cos2胃 is obtained by compressing the the graph of r=cos胃by factor of 12horizontally then compress the graph vertcally by a factor of 12then vertcally shift the graph by 12units upward.

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Most popular questions from this chapter

Use polar coordinates to graph the conics in Exercises 44鈥�51.

r=22+sin胃

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�-蟺2蟺2(2-sin胃)2d胃

Sketch the graphs of the equations

r=11+cos胃and localid="1649854142659" r=11+sin胃

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

Use polar coordinates to graph the conics in Exercises 44鈥�51.

r=21-3cos胃

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

3,-3
See all solutions

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