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Chapter 7: Q. 44 (page 465)

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

tan胃2=-1

Short Answer

Expert verified

A general formula for all the solutions is 胃=3蟺2+2苍蟺and list of six solution of the given equation is 3蟺2,7蟺2,11蟺2,15蟺2,19蟺2,23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.

tan胃2=-1

02

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

In the interval [0,蟺), the tangent function equals -1at 3蟺4

To find these solutions, write the general formula that gives all the solutions.

role="math" localid="1646757172774" 胃2路2=2路3蟺4+苍蟺胃=2路3蟺4+2路苍蟺胃=3蟺2+2苍蟺

03

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

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

Six of the solutions are

3蟺2,7蟺2,11蟺2,15蟺2,19蟺2,23蟺2

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Most popular questions from this chapter

If tan胃=atan胃3, expresstan胃3in terms of a.

Establish each identity.

1+sin胃1-sin胃-1-sin胃1+sin胃=4tan胃sec胃

True or False:tan胃cos胃=sin胃for any胃鈮�(2k+1)蟺2

If x=2tan胃, express cos2胃as a function ofx.

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

cotsin-1-12
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