Problem 85 - Algebra and Trigonometry

Question

Use words to describe the formula for: the power-reducing formula for the sine squared of an angle.

Step-by-Step Solution

Answer

The power-reducing formula for the sine squared of an angle is given by: \(\sin^2(x) = \frac{1 - \cos(2x)}{2}\). It is calculated by taking away the cosine of twice the angle from one and then half of this result gives us the sine squared of the angle.

Step 1: Identify the main elements

We have two main elements in this formula: \(\sin^2(x)\) which is the sine of an angle squared and \(\cos(2x)\) which is the cosine of twice the angle.

Step 2: Link the main elements together

A power-reducing formula calculates the sine squared of an angle by using the cosine of twice that angle. The formula accomplishes this by one subtracting the cosine of twice the angle from one, and then dividing the result by two.

Step 3: Give a summarized explanation

Therefore, the power-reducing formula for the sine squared of an angle is obtained by subtracting the cosine of twice the angle from one and dividing the result by two.