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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 41. (page 457)

In Problems $37 - 44$ , find the exact value of each expression.
role="math" localid="1646484604880" $s e c^{- 1} \frac{2 \sqrt{3}}{3}$

Short Answer

Expert verified

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

Step by step solution

01

Step 1. Write the given information

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

02

Use the trigonometric identity,

We know that $s e c x = \frac{1}{\cos x}$

Therefore we get:

$\frac{1}{\cos x} = \frac{2 \sqrt{3}}{3} \cos x = \frac{3}{2 \sqrt{3}} \cos x = \frac{3}{2 \sqrt{3}} 路 \frac{\sqrt{3}}{\sqrt{3}} \cos x = \frac{3 \sqrt{3}}{6} \cos x = \frac{\sqrt{3}}{2}$

$x = \cos^{- 1} \frac{\sqrt{3}}{2} x = \cos^{- 1} (\cos \frac{蟺}{6}) x = \frac{蟺}{6}$

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