Question

Express as a sum or difference. $$\sin (-4 x) \cos 8 x$$

   Express as a sum or difference.
$$\sin (-4 x) \cos 8 x$$

Precalculus: Functions and Graphs

Precalculus: Functions and Graphs

Earl W. Swokowski,… 11th Edition

Chapter 6, Problem 2

Instant Answer

Solved by Expert Wendi Zhao

05/21/2021

Step 1

In this case, we need the product-to-sum formula for sine and cosine, which is given by: $$\sin(u) \cos(v) = \frac{1}{2}[\sin(u+v) + \sin(u-v)]$$ Show more…

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Express as a sum or difference. $$\sin (-4 x) \cos 8 x$$

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Key Concepts

Product-to-Sum Identities

Product-to-sum identities are formulas used to rewrite products of trigonometric functions as sums or differences. They simplify the task of integrating or analyzing trigonometric expressions by converting a product into a sum or difference of sine and cosine functions.

Even-Odd Properties of Trigonometric Functions

The even-odd properties of trigonometric functions help simplify expressions by taking advantage of symmetry. Specifically, sine is an odd function (meaning sin(-?) = -sin(?)) and cosine is an even function (cos(-?) = cos(?)). These properties are essential for correctly transforming expressions that involve negative angles.

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