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Chapter 9: Q. 40 (page 747)

For each pair of functions in Exercises 40鈥�45, (a) Algebraically find all values of 胃wheref1胃=f2胃 (b) Sketch the two curves in the same polar coordinate system. (c) Find all points of intersection between the two curves. 40.f1(胃)=sin2胃andf2(胃)=鈭�sin2胃.

Short Answer

Expert verified

Part (a)胃=n蟺2

Part (c) 卤蟺2,0;卤蟺,0...

Part (b)

Step by step solution

01

Part (a) Step 1. Given Information.

The two curves are :

f1(胃)=sin2胃andf2(胃)=鈭�sin2胃.

02

Part (a) Step 2. Algebraically.

When

f1胃=f2胃sin2胃=-sin2胃sin2胃+sin2胃=02sin2胃=0sin2胃=0sin胃=sin0=n蟺2胃=n蟺胃=n蟺2.

03

Part (b) Step 1. Sketching the curves.

Consider the given information from part (a).

The two curves are :

04

Part (c)  Step 1. Point of intersection.

Consider the given information from part (a).

The points of intersection between the curves are

f1胃=f2胃sin2胃=-sin2胃sin2胃+sin2胃=02sin2胃=0sin2胃=0sin胃=sin0=n蟺2胃=n蟺胃=n蟺2.

So, Points are 卤蟺2,0;卤蟺,0,..

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Most popular questions from this chapter

Measurements indicate that Earth鈥檚 orbital eccentricity is 0.0167and its semimajor axis is 1.00000011astronomical units.

(a) Write a Cartesian equation for Earth鈥檚 orbit.

(b) Give a polar coordinate equation for Earth鈥檚 orbit, assuming that the sun is the focus of the elliptical orbit.

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

r=11-cos胃

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=胃for0鈮�胃鈮�2蟺

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

1,0

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?
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