Problem 83 - Algebra and Trigonometry

Question

Use words to describe the formula for: the cosine of double an angle. (Describe one of the three formulas.)

Step-by-Step Solution

Answer

The cosine of double an angle formula \( \cos(2A) \) can be described as the square of the cosine of the original angle subtracted by the square of the sine of the original angle, where \( A \) is the original angle.

Step 1: Understanding the Formula Symbols

The formula \( \cos(2A) = \cos^2(A) - \sin^2(A) \) has a few key symbols. The symbol \( \cos(2A) \) represents the cosine of an angle that is twice the size of angle A. The \( \cos^2(A) \) and \( \sin^2(A) \) symbols represent the square of the cosine and sine of angle A respectively.

Step 2: Understanding the Formula Construction

The formula is structured such that the term \( \cos^2(A) - \sin^2(A) \) represents the value of \( \cos(2A) \) . Essentially, to find the cosine of a doubled angle, one can square the cosine of the angle and subtract the square of the sine of the angle.

Step 3: Usage of the Formula

This formula is used when one needs to find the cosine of an angle that is twice as large as a known angle. The values for the sine and cosine of the original angle are placed in the formula to calculate the final result.