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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 7: Q. 1 (page 505)

Find the exact value of the expression. Express angles in radians.
$s e c^{- 1} (\frac{2}{\sqrt{3}})$

Short Answer

Expert verified

The exact value of the given expression is $\frac{蟺}{6}$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$s e c^{- 1} (\frac{2}{\sqrt{3}})$

Assume $胃 = s e c^{- 1} (\frac{2}{\sqrt{3}})$ .

As $y = \sin^{- 1} x$ means $x = \sin y$ , where,

$- \frac{蟺}{2} 鈮� 胃鈮� \frac{蟺}{2}$

Rewrite the function,

$s e c 胃 = \frac{2}{\sqrt{3}}$

02

Step 2. Use the reciprocal identity.

Using the reciprocal identity, $s e c 胃 = \frac{1}{\cos 胃}$ ,

Then,

$\frac{1}{\cos 胃} = \frac{1}{\frac{2}{\sqrt{3}}} \cos 胃 = \frac{\sqrt{3}}{2}$

We know $\cos \frac{蟺}{6} = \frac{\sqrt{3}}{2}$ and as $\frac{蟺}{6}$ is in the interval $0 鈮� 胃鈮� 蟺$ .

Then, we can say,

localid="1646501788181" $\cos 胃 = \cos \frac{蟺}{6} 胃 = \frac{蟺}{6}$

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Most popular questions from this chapter

True or False : In establishing an identity, it is often easiest to just multiply both sides by a well-chosen nonzero expression involving the variable.

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

$\cos [\sin^{- 1} (- \frac{\sqrt{3}}{2})]$

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

$\sin \frac{蠎}{2} \cos \frac{5 蠎}{2}$

If $\tan 伪 = x + 1$ and role="math" localid="1646425111199" $\tan 尾 = x - 1,$ show that

role="math" localid="1646426027733" $2 c o t (伪 - b) = x^{2}$

Establish each identity.

$\frac{s e c^{2} v - \tan^{2} v + \tan v}{s e c v} = \sin v + \cos v$

See all solutions

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