Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q 68. (page 458)

In problem, $f (x) = \sin x, - \frac{蟺}{2} 鈮� x 鈮� \frac{蟺}{2}, g (x) = \cos x, 0 鈮� x 鈮� 蟺$ and $h (x) = \tan x, - \frac{蟺}{2} 鈮� x 鈮� \frac{蟺}{2}$ . Find the exact value of the composite function.
$\begin{array}{rcl} f (g^{- 1} (\frac{5}{13})) \end{array}$

Short Answer

Expert verified

Value of the composite function is $\frac{12}{13}$ .

Step by step solution

Step 1. Given information

$f (x) = \sin x, - \frac{蟺}{2} 鈮� x 鈮� \frac{蟺}{2}, g (x) = \cos x, 0 鈮� x 鈮� 蟺$ and $h (x) = \tan x, - \frac{蟺}{2} 鈮� x 鈮� \frac{蟺}{2}$

Step 2. Value of the composite function.

It is given that $g (x) = \cos x$ .

$g^{- 1} (\frac{5}{13}) = \cos^{- 1} (\frac{5}{13})$

Let $\cos^{- 1} (\frac{5}{13}) = y$

$\cos y = \frac{5}{13}$

Consider the following figure:

Side opposite to $y = \sqrt{{(13 k)}^{2} - {(5 k)}^{2}}$

$= \sqrt{169 k^{2} - 25 k^{2}} = 12 k$

So,

localid="1646637094118" $\begin{array}{rcl} \sin y & = & \frac{12 k}{13 k} \\ = & \frac{12}{13} \end{array}$

Therefore,

localid="1647840098492" $\begin{array}{rcl} f (g^{- 1} (\frac{5}{13})) & = & \sin (\sin^{- 1} (\frac{12}{13})) \\ = & \frac{12}{13} \end{array}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In problem, $f (x) = \sin x, - \frac{蟺}{2} 鈮� x 鈮� \frac{蟺}{2}, g (x) = \cos x, 0 鈮� x 鈮� 蟺$ and $h (x) = \tan x, - \frac{蟺}{2} 鈮� x 鈮� \frac{蟺}{2}$ . Find the exact value of the composite function.
$\begin{array}{rcl} f (g^{- 1} (\frac{5}{13})) \end{array}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Value of the composite function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Logic and Functions

Calculus

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

In problem, f(x)=sinx,-蟺2鈮�x鈮�蟺2,g(x)=cosx,0鈮�x鈮�蟺and h(x)=tanx,-蟺2鈮�x鈮�蟺2. Find the exact value of the composite function.fg-1513

Short Answer

Step by step solution

Step 1. Given information

Step 2. Value of the composite function.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Logic and Functions

Calculus

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

In problem, $f (x) = \sin x, - \frac{蟺}{2} 鈮� x 鈮� \frac{蟺}{2}, g (x) = \cos x, 0 鈮� x 鈮� 蟺$ and $h (x) = \tan x, - \frac{蟺}{2} 鈮� x 鈮� \frac{蟺}{2}$ . Find the exact value of the composite function.
$\begin{array}{rcl} f (g^{- 1} (\frac{5}{13})) \end{array}$