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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.37 (page 395)

$\sin 胃, \cos 胃$ are given.Find the exact value of each of the four remaining trigonometric functions localid="1646650767506" role="math" $\sin 胃 = \frac{2 \sqrt{5}}{5} a n d \cos 胃 = \frac{\sqrt{5}}{5}$

Short Answer

Expert verified

The value of $c s c 胃 = \frac{5}{2 \sqrt{5}}, s e c 胃 = \frac{5}{\sqrt{5}}, \tan 胃 = 2 a n d c o t 胃 = \frac{1}{2}$

Step by step solution

01

Step 1. Given information

$\sin 胃 = \frac{2 \sqrt{5}}{5} a n d \cos 胃 = \frac{\sqrt{5}}{5}$

are given.

We have to find out the exact value of each of the four remaining trigonometric functions.

02

. Finding the value of trigonometric functions cscθ and secθ

In this question

$\sin 胃 = \frac{2 \sqrt{5}}{5} s o c s c 胃 = \frac{1}{\sin 胃} = \frac{1}{\frac{2 \sqrt{5}}{5}} = \frac{5}{2 \sqrt{5}} \cos 胃 = \frac{\sqrt{5}}{5} t h e n s e c 胃 = \frac{1}{\cos 胃} = \frac{1}{\frac{\sqrt{5}}{5}} = \frac{5}{\sqrt{5}}$

03

Step 3. Finding the value of trigonometric function tanθ and cotθ

We know that

$\tan 胃 = \frac{\sin 胃}{\cos 胃} = \frac{\frac{2 \sqrt{5}}{5}}{\frac{\sqrt{5}}{5}} \sin c e \sin 胃 = \frac{2 \sqrt{5}}{5} a n d \cos 胃 = \frac{\sqrt{5}}{5} = 2 a n d c o t 胃 = \frac{1}{\tan 胃} = \frac{1}{2}$

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Most popular questions from this chapter

What is the formula for the circumference $C$ of a circle of radius $r$ ? What is the formula for the area $A$ of a circle of radius $r$ ?

In Problems 13鈥�20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

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