Question

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

Answer 1

Because the identity uses squares (e.g., sin^2 x + cos^2 x = 1), taking a square root to solve for one function returns both +√(…) and −√(…) since squaring removes sign information. Which sign is correct depends on the angle’s quadrant (where sine and cosine can be positive or negative).