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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 109. (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 $(f 路 g) (\frac{3 蟺}{4})$ .

Short Answer

Expert verified

The value of $(f 路 g) (\frac{3 蟺}{4})$ is $- \frac{1}{2}$ .

Step by step solution

01

Step 1. Given information.

Given $f (x) = \sin x$ and $g (x) = \cos x$ and the value of $x$ is $\frac{3 蟺}{4}$ .

02

Step 2. Simplify the given expression.

$(f 路 g) 路 (\frac{3 蟺}{4})$ can be written as $f (\frac{3 蟺}{4})$ and $g (\frac{3 蟺}{4})$ .

Substitute $\sin (\frac{3 蟺}{4})$ for $f (\frac{3 蟺}{4})$ and $\cos (\frac{3 蟺}{4})$ for $g (\frac{3 蟺}{4})$ .

then,

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

03

Step 3. Find the value of f·g 3π4.

In trigonometric standard angle the value of $\sin (\frac{3 蟺}{4})$ is $\frac{1}{\sqrt{2}}$ and the value of $\cos (\frac{3 蟺}{4})$ is $- \frac{1}{\sqrt{2}}$ .

Substitute the values of angles in simplified expression.

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

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Most popular questions from this chapter

True or false The function $f (x) = \sqrt{x}$ is even.

In problems 13-20, $P (x, y)$ is the point on the unit circle that corresponds to a real number $t$ . Find the exact values of the six trigonometric functions of $t$ .

$(- \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ .

A function for which $f (x) = f (- x)$ for all $x$ in the domain of $f$ is called a(n) ___ function.

Convert each angle to a decimal in degrees. Round your answer to two decimal places.

$40 掳 10' 25''$

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

$- 135 掳$

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