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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 6: Q 116. (page 382)

If $f (x) = \sin x, g (x) = \cos x,$ and $h (x) = 2 x, P (x) = \frac{x}{2}$ then find the values of points given below.
(a) Find $g (\frac{蟺}{6})$ .What point is on the graph of g.
(b) Assuming g one to one use the result of part (a) to find a point on the graph of $g^{- 1}$ .
(c) What point is on the graph of $y = 2 g (x - \frac{蟺}{6})$ if $x = \frac{蟺}{6}$

Short Answer

Expert verified

(a) Value of $g (\frac{蟺}{6})$ is $\frac{\sqrt{3}}{2}$ .

(b) $g^{- 1} = \frac{2}{\sqrt{3}}$

(c) $y = 0$

Step by step solution

01

Step 1. Given information .

Consider the given value $g (x) = \cos x$ where $x = \frac{蟺}{6}$ .

02

Step 2. Finding g=π6.

Substitute $g (\frac{蟺}{6}) = \cos \frac{蟺}{6}$ in function $g (x) = \cos x$ . In trigonometric standard angle the value of $\cos \frac{蟺}{6} = 30 掳 = \frac{\sqrt{3}}{2}$ so,

$g (\frac{蟺}{6}) = \cos \frac{蟺}{6} = \frac{\sqrt{3}}{2}$

03

Step 3. Plot the graph.

The graph for $g (\frac{蟺}{6})$ is shown below.

04

Step 4. (b) Finding g-1.

$g^{- 1} = \frac{1}{g} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}}$

05

Step 5.(c) Finding a point on the graph .

Substitute the value of $x$ in function $y = 2 g (x - \frac{蟺}{6})$

$y = 2 脳 g (\frac{蟺}{6} - \frac{蟺}{6}) y = 0$

The graph for $y = 0$ shown below.

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Most popular questions from this chapter

In the problem, $s$ denotes the length of the arc of a circle of radius $r$ subtended by the central angle $胃$ . Find the missing quantity. Round answers to three decimal places.

$r = 10$ meters, $胃 = \frac{1}{2}$ radian, $s = ?$

Find the exact value of each expression. Do not use a calculator.

$2 \sin \frac{蟺}{4} + 3 \tan \frac{蟺}{4}$

Find the exact value of each expression. Do not use a calculator.

$2 \sec \frac{蟺}{4} + 4 \cot \frac{蟺}{3}$

Convert each angle in degrees to radians. Express your answer as a multiple of $蟺$ .

$240 掳$

the point (x, y) is on the terminal side of angle $蠎$ in standard position. Find the exact value of the given trigonometric function

$(2, 7), \sin 蠎$

See all solutions

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