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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 6: Q.84 (page 396)

use properties of the trigonometric functions to find the exact value of each expression. Do not use a calculator:
$\tan (200^{o}) \cot (20^{o})$

Short Answer

Expert verified

The exact value of $\tan (200^{o}) \cot (20^{o}) i s 1$

Step by step solution

01

Given information

We are given a trigonometric equation $\tan (200^{o}) \cot (20^{o})$

02

use periodicity of the trigonometric functions tanθ+π=tanθ

We get

$\tan (200^{o}) \cot (20^{o}) \tan (180^{o} + 20^{0}) \cot (20^{o}) \tan (20^{o}) \cot (20^{o}) \tan (200^{o}) \frac{1}{\tan (20^{o})} = 1$

03

Conclusion

The exact value of $\tan (200^{o}) \cot (20^{o}) i s 1$

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