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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 7: Q. 104 (page 498)

Find the value of the number C:
$\frac{1}{2} \cos^{2} x + C = \frac{1}{4} \cos (2 x)$

Short Answer

Expert verified

The value of C is $- \frac{1}{4}$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$\frac{1}{2} \cos^{2} x + C = \frac{1}{4} \cos (2 x) . . . . . . (i)$

From the double-angle formulas,

$\cos (2 胃) = 2 \cos^{2} 胃 - 1$

From equation (i),

$\frac{1}{2} \cos^{2} x + C = \frac{1}{4} \cos (2 x) C = \frac{1}{4} \cos (2 x) - \frac{1}{2} \cos^{2} x$

02

Step 2. Simplify the equation.

We know $\cos 2 x = 2 \cos^{2} x - 1$ , then

localid="1646414862206" $C = \frac{1}{4} (2 \cos^{2} x - 1) - \frac{1}{2} c {os}^{2} x C = \frac{2}{4} \cos^{2} x - \frac{1}{4} - \frac{1}{2} c {os}^{2} x C = \frac{1}{2} \cos^{2} x - \frac{1}{4} - \frac{1}{2} c {os}^{2} x C = - \frac{1}{4}$

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