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Chapter 7: Q. 6 (page 503)

In Problems 1鈥� 8, find the exact value of each expression. Do not use a calculator.

tan-1(-3)

Short Answer

Expert verified

The exact value is -蟺3.

Step by step solution

01

Step 1. Definition 

The inverse tangent function y=tan-1xmeans that x=tanywhere -鈭�<x<鈭�and -蟺2<y<蟺2.

02

Step 2. Find the exact value 

Let 胃=tan-1(-3), so using the definition of inverse tangent function it can be written as -3=tan胃where -蟺2<胃<蟺2.

In this interval the angle for which the tangent value is -3is -蟺3.

So the value of tan-1(-3)is -蟺3.

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Most popular questions from this chapter

Establish each identity.

1+sin胃1-sin胃-1-sin胃1+sin胃=4tan胃sec胃


express each product as a sum containing only sines or only cosines

sin蠎sin2蠎

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

cossin-122

Establish each identity.

1+cos胃+sin胃1+cos胃-sin胃=sec胃+tan胃

solve each equation on the interval 0鈮�胃<2蟺

sin胃-3cos胃=1
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