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Chapter 6: Problem 82

Use words to describe the formula for each of the following: the cosine of the sum of two angles.

Short Answer

Expert verified
The formula for the cosine of the sum of two angles is \( \cos(A + B) = \cos(A)\cos(B) - \sin(A)\sin(B) \), where \( \cos(A + B) \) represents the cosine of the sum of two angles A and B, and the right side illustrates the cosine of A times the cosine of B subtracted by the sine of A times the sine of B.

Step by step solution

01

Identify the formula

The first step is to identify the correct formula. The formula for the cosine of the sum of two angles (denoted as \( \cos(A + B) \)) is \( \cos(A + B) = \cos(A)\cos(B) - \sin(A)\sin(B) \).
02

Break down the formula

The second step is to break down different parts of the formula. The term \( \cos(A + B) \) represents the cosine of the sum of two angles A and B. The right side of the equation \( \cos(A)\cos(B) - \sin(A)\sin(B) \) includes two parts - the cosine of A times the cosine of B ( \( \cos(A)\cos(B) \)) and minus the sine of A times the sine of B ( \( \sin(A)\sin(B) \)).
03

Explain the significance of the formula

This formula is significant as it allows us to convert the cosine of a sum of two angles into a simple form involving the cosines and sines of the original angles, making computations easier in various mathematical and physical contexts.

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