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Chapter 6: Problem 83

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

Short Answer

Expert verified
The sine of the sum of two angles is equal to the sum of the product of the sine of the first angle and the cosine of the second angle, and the product of the cosine of the first angle and the sine of the second angle.

Step by step solution

01

Understanding the Problem

First, it is important to understand that we are required to describe the mathematical formula for the sine of the sum of two angles. This formula is widely used in trigonometry and represents the sine of the sum of two angles in terms of the sines and cosines of the two angles.
02

Defining the Formula in Symbols

The mathematical expression for this is written as \( \sin(A + B) = \sin A \cos B + \cos A \sin B \). Here, 'A' and 'B' are angles and 'sin' refers to the sine of the angle, while 'cos' refers to the cosine of the angle.
03

Describing the Formula in Words

We can describe this formula in words as follows: 'The sine of the sum of two angles \(A\) and \(B\) is equal to the sum of the product of the sine of angle \(A\) and cosine of angle \(B\) and the product of the cosine of angle \(A\) and the sine of angle \(B\).' Understanding this description is crucial to applying this formula in trigonometric problems.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I solved \(4 \cos ^{2} x=5-4 \sin x\) by working independently with the left side, applying a Pythagorean identity, and transforming the left side into \(5-4 \sin x .\)

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

Use a calculator to solve each equation, correct to four decimal places, on the interval \([0,2 \pi)\) $$ 7 \sin ^{2} x-1=0 $$

Use the most appropriate method to solve each equation on the interval \([0,2 \pi) .\) Use exact values where possible or give approximate solutions correct to four decimal places. $$ 7 \cos x=4-2 \sin ^{2} x $$

Use words to describe the formula for each of the following: the sine of the difference of two angles.
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