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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 50. (page 457)

In Problems 45鈥�56, use a calculator to find the value of each expression rounded to two decimal places.
$c o t^{- 1} (- \frac{1}{2})$

Short Answer

Expert verified

The value of the given expression in two decimal places is $- 1.11$

Step by step solution

01

Step 1. Write the given information.

$c o t^{- 1} (- \frac{1}{2})$

02

Step 2. Rewrite the given expression.

The given expression can be rewritten as:

$c o t^{- 1} (- \frac{1}{2}) = x$

We apply the $c o t$ function on both sides so we get:

$c o t (c o t^{- 1} (- \frac{1}{2})) = c o t x c o t x = - \frac{1}{2}$

03

Step 3. Use the trigonometric identity.

We know that

$c o t x = \frac{1}{\tan x} \frac{1}{\tan x} = - \frac{1}{2} \tan x = - 2$

We apply the $\tan^{- 1}$ function on both sides we get:

$\tan^{- 1} (\tan x) = \tan^{- 1} (- 2) x = \tan^{- 1} (- 2)$

04

Step 4. Use the calculator to find the value.

$x = - 1.11 c o t^{- 1} (- \frac{1}{2}) = - 1.11$

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