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Chapter 7: Q. 39 (page 465)

In Problems 35鈥� 44, solve each equation. Give a general formula for all the solutions. List six solutions

cos胃=0

Short Answer

Expert verified

A general formula for all the solutions is 胃|蟺2+2n蟺,3蟺2+2苍蟺and list of six solution of the given equation is 蟺2,3蟺2,5蟺2,7蟺2,9蟺2,11蟺2.

Step by step solution

01

Step 1. Given Information 

In the given problems we have to solve each equation. Give a general formula for all the solutions. List six solutions.

cos胃=0

02

Step 2. The period of the cosine function is 2π.

In the interval [0,2蟺), there are two angles 胃for which

cos胃=0:胃=蟺2

Because the cosine function has period 2蟺, all the solutions of may be cos胃=0given by the general formula

localid="1646754520411" 胃=蟺2+2n蟺or胃=3蟺2+2苍蟺

03

Step 3. The general formula is θ=π2+2nπ        or        θ=3π2+2nπ

We find the six solutions by puttingn=1,2,3,........ in general formula

Six of the solutions are

蟺2,3蟺2,5蟺2,7蟺2,9蟺2,11蟺2

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Most popular questions from this chapter

Rewrite in terms of sine and cosine functions:tan胃csc胃

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