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Chapter 9: Q. 15 (page 747)

Finish Example 1 by showing that r=cos2胃is symmetrical with respect to the horizontal axis.

Short Answer

Expert verified

It has been proved that the curve is symmetrical about the horizontal axis.

Step by step solution

01

Step 1. Given information

Equation of polar curve:

r(胃)=cos2胃

02

Step 2. Show the symmetry with respect to the horizontal axis.

If r-胃=r胃then the curve is symmetrical about the x-axis.

r(胃)=cos2胃r-胃=cos2-胃r-胃=cos-2胃r-胃=cos2胃r-胃=r(胃)

Hence the given curve is symmetrical about the horizontal axis.

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Most popular questions from this chapter

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

r=24+cos胃

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

r2=cos胃

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

x=4

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

directrixy=0,focus(0,1)
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