Problem 81 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

The formula to find the cosine of the difference of two angles is \( cos(A-B) = cosAcosB + sinAsinB \), where 'A' and 'B' are the two angles.

Step 1: Recall of formula

Firstly recall the cosine of difference of two angles formula from trigonometry. The formula is \( cos(A-B) = cosAcosB + sinAsinB \).

Step 2: Explanation of the formula

In the formula, 'A' and 'B' stand for the two angles in question. The Cosine of the difference of angles 'A' and 'B' can be computed by taking the Cosine of angle 'A' and multiplying it by the Cosine of angle 'B', and then adding the product of the sine of angle 'A' and the sine angle 'B'.

Step 3: Example

For instance, if you're finding the cosine of the differences of 60° and 45°. Fill in for 'A' is 60° and 'B' is 45° into the formula to get \( cos(60 - 45) = cos(60)cos(45) + sin(60)sin(45) \), which would give the result.