Problem 83 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

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 1: 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.

Step 2: 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.

Step 3: 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.