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Chapter 7: Q. 71 (page 496)

In Problems 69-78, solve each equation on the interval 0鈮�胃<2蟺.

cos2胃=cos胃.

Short Answer

Expert verified

The solution set for the equationcos2胃=cos胃is,0,2蟺3,4蟺3.

Step by step solution

01

Step 1 Given equation is,

cos2胃=cos胃.

The double angle formula for cos2胃is, cos2胃=2cos2胃-1

Substitute the known values in the given equation.

2cos2胃-1=cos胃2cos2胃-1-cos胃=0

02

Step 2 Factor the expression.

cos胃-12cos胃+1=0cos胃-1=0or2cos胃+1=0cos胃=1or2cos胃=-1cos胃=1orcos胃=-12

In the interval [0,2蟺)cos胃has value 1for 胃=0and has value -12for 胃=2蟺3,4蟺3.

Therefore the solution set is,0,2蟺3,4蟺3.

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Most popular questions from this chapter

True or False

tan2胃=2tan胃1-tan2胃

In Problems 9鈥�36, find the exact value of each expression.

csccos-1-32

Establish each identity.

1+cos胃+sin胃1+cos胃-sin胃=sec胃+tan胃

find the exact value of the expression

sin 285掳sin 75掳

A rectangle is inscribed in a semicircle of radius 1. See the illustration.

Part (a): Express the area A of the rectangle as a function of the angle 胃shown in the illustration.

Part (b): Show that A胃=sin2胃.

Part (c): Find the angle 胃 that results in the largest area A.

Part (d): Find the dimensions of this largest rectangle.
See all solutions

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