Question

In 1–2 sentences, describe why there is always a positive and negative solution when solving using the Pythagorean Identity.

Answer 1

The Pythagorean Identity, sin²(θ) + cos²(θ) = 1, represents a circular relationship on the unit circle, where for each angle θ, both the sine and cosine values can be positive or negative depending on the quadrant in which the angle lies. Therefore, for any given sine or cosine value derived from the identity, there are always both positive and negative solutions corresponding to the possible quadrants.