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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 114. (page 382)

If $f (x) = \sin x, g (x) = \cos x$ and $h (x) = 2 x, P (x) = \frac{x}{2}$ .Find the value of $(h 路 f) (\frac{5 蟺}{6})$ .

Short Answer

Expert verified

The value of $(h 路 f) (\frac{5 蟺}{6})$ is $\frac{5 蟺}{6}$ .

Step by step solution

01

Step 1. Given information.

Given $h (x) = 2 x$ role="math" localid="1646553814626" $, f (x) = \sin x$ and the value of $x$ is $\frac{5 蟺}{6}$ .

02

Step 2. Simplify the given expression.

$(h 路 f) (\frac{5 蟺}{6})$ can be written as $h (\frac{5 蟺}{6})$ and $f (\frac{5 蟺}{6})$ .

Substitute $2 x$ for $h (\frac{5 蟺}{6})$ and $\sin x$ for $f (\frac{5 蟺}{6})$ .

$(h 路 f) (\frac{5 蟺}{6}) = (2 脳 \frac{5 蟺}{6} 路 \sin \frac{5 蟺}{6})$

03

Step 3. Find the valuer of h·f 5π6.

In trigonometric standard angle the value of $\sin \frac{5 蟺}{6}$ is $\frac{1}{2}$ .

Substitute the value in the simplified expression.

$(h 路 f) (\frac{5 蟺}{6}) = (2 脳 \frac{5 蟺}{6} 路 \sin \frac{5 蟺}{6}) = (\frac{5 蟺}{3} 路 \frac{1}{2}) = \frac{5 蟺}{6}$

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Most popular questions from this chapter

Find the exact values of the six trigonometric functions of the given angle. If any are not defined, say "not defined." Do not use a calculator.

$\frac{2 蟺}{3}$

Convert angle in radian to degree-

$4 蟺$

The equation $x^{2} + 2 x = {(x + 1)}^{2} - 1$ is an identity.

Convert angle in radian to degree-

$\frac{5 蟺}{6}$

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

$- 90 掳$

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