Chapter 7: Q. 10 (page 503)

In Problems 9–23, find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.
$\cos^{- 1} (\cos \frac{3 π}{4})$

Short Answer

Expert verified

The exact value is $\frac{3 π}{4}$ .

Step by step solution

Step 1. Given Information

We are given a composite function $\cos^{- 1} (\cos \frac{3 π}{4})$ .

We need to find its exact value.

Step 2. Concept used

The cosine function and its inverse, form these properties

$\cos^{- 1} (\cos x) = x$ where $0 \leq x \leq π$

and

$\cos (\cos^{- 1} x) = x$ where $- 1 \leq x \leq 1$

Step 3. Find the exact value

As $\frac{3 π}{4}$ lies in the interval $[0, π]$ . So using the property formed by cosine and its inverse function we have

$\cos^{- 1} (\cos \frac{3 π}{4}) = \frac{3 π}{4}$

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In Problems 9–23, find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.
$\cos^{- 1} (\cos \frac{3 π}{4})$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept used

Step 3. Find the exact value

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In Problems 9–23, find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator. cos-1cos3π4

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Concept used

Step 3. Find the exact value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems 9–23, find the exact value, if any, of each composite function. If there is no value, say it is “not defined.” Do not use a calculator.
$\cos^{- 1} (\cos \frac{3 π}{4})$