Q. 24 Express each sum or difference a... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 24 (page 500)

Express each sum or difference as a product of sines and/or cosines.
$\sin \frac{胃}{2} - \sin \frac{3 胃}{2}$

Short Answer

Expert verified

The required product is $- 2 \sin (\frac{胃}{2}) \cos 胃$ .

Step by step solution

Step 1. Given Information

We are given with the expression $\sin \frac{胃}{2} - \sin \frac{3 胃}{2}$ and we need to express it as a product in terms of sines and cosines.

Step 2. Using the formula

The standard formula is $\sin 伪 - \sin 尾 = 2 \sin (\frac{伪 - 尾}{2}) \cos (\frac{伪 + 尾}{2})$ .

Comparing it with the given equation $\sin \frac{胃}{2} - \sin \frac{3 胃}{2}$ we get, $伪 = \frac{胃}{2}, 尾 = \frac{3 胃}{2}$ .

Substituting $伪, 尾$ in the standard formula,

$\sin \frac{胃}{2} - \sin \frac{3 胃}{2} = 2 \sin (\frac{\frac{胃}{2} - \frac{3 胃}{2}}{2}) \cos (\frac{\frac{胃}{2} + \frac{3 胃}{2}}{2}) = 2 \sin (\frac{- \frac{2 胃}{2}}{2}) \cos (\frac{\frac{4 胃}{2}}{2}) = 2 \sin (- \frac{胃}{2}) \cos (\frac{2 胃}{2}) = 2 \sin (- \frac{胃}{2}) \cos 胃$

Step 3. Using even-odd identities

We know, $\sin (- 胃) = - \sin 胃$ .

$鈭� \sin \frac{胃}{2} - \sin \frac{3 胃}{2} = 2 \sin (- \frac{胃}{2}) \cos 胃 = - 2 \sin (\frac{胃}{2}) \cos 胃$

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91影视

Express each sum or difference as a product of sines and/or cosines.
$\sin \frac{胃}{2} - \sin \frac{3 胃}{2}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Using the formula

Step 3. Using even-odd identities

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91影视

Express each sum or difference as a product of sines and/or cosines.sin胃2-sin3胃2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Using the formula

Step 3. Using even-odd identities

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Mechanics Maths

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

Express each sum or difference as a product of sines and/or cosines.
$\sin \frac{胃}{2} - \sin \frac{3 胃}{2}$