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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 111. (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 $(f 路 h) (\frac{蟺}{6})$ .

Short Answer

Expert verified

The value of $(f 路 g) (\frac{蟺}{6})$ is $\frac{\sqrt{3}}{4}$ .

Step by step solution

01

Step 1. Given information.

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

02

Step 2. Simplify the given expression.

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

Substitute $\sin (\frac{蟺}{6})$ for $f (\frac{蟺}{6})$ and $\cos (\frac{蟺}{6})$ for $g (\frac{蟺}{6})$ .

then,

$(f 路 g) (\frac{蟺}{6}) = (\sin \frac{蟺}{6} 路 \cos \frac{蟺}{6})$

03

Step 3. Find the value of f·g π6.

In trigonometric standard angle the value of $\sin (\frac{蟺}{6})$ is $\frac{1}{2}$ and the value of $\cos (\frac{蟺}{6})$ is $\frac{\sqrt{3}}{2}$ .

Substitute the values in simplified expression.

$(f 路 g) (\frac{蟺}{6}) = (\sin \frac{蟺}{6} 路 \cos \frac{蟺}{6}) = (\frac{1}{2} 路 \frac{\sqrt{3}}{2}) = (\frac{\sqrt{3}}{4})$

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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.

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