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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 48. (page 457)

In Problems 45鈥�56, use a calculator to find the value of each expression rounded to two decimal places.
$s e c^{- 1} (- 3)$

Short Answer

Expert verified

The value of the given expression in two decimal places is $1.91$

Step by step solution

01

Step 1. Write the given information.

$s e c^{- 1} (- 3)$

02

Step 2. Rewrite the given expression.

The given expression can be rewritten as:

$s e c^{- 1} (- 3) = x$

We apply the $s e c$ function on both sides so we get:

$s e c (s e c^{- 1} (- 3)) = s e c x s e c x = - 3$

03

Step 3. Use the trigonometric identity.

We know that $s e c x = \frac{1}{\cos x}$ therefore we get:

$\frac{1}{\cos x} = - 3 \cos x = - \frac{1}{3}$

Apply the $\cos^{- 1}$ function on both sides we get:

$\cos^{- 1} (\cos x) = \cos^{- 1} (- \frac{1}{3}) x = \cos^{- 1} (- \frac{1}{3})$

04

Step 4. Use the calculator and find the value.

$x = 1.91 s e c^{- 1} (- 3) = 1.91$

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Most popular questions from this chapter

True or False. $\sin (2 胃)$ has two equivalent forms:

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