Given that cosθ=0.2588 and 0< θ < π, use the Pythagorean identity to find sinθ.

Question

Given that cosθ=0.2588 and 0< θ < π, use the Pythagorean identity to find sinθ.

Answer 1

The Pythagorean Identity is

sin² x + cos² x = 1

sin² x + 0.2588² = 1

Solve for sin x.

Answer 2

Let's say that the hypotenuse has length 1. Since cosθ is 0.2588, that makes the adjacent side length 0.2588. Using the pythagorean formula, we can calculate the opposite side length to be 0.9659. So sinθ must be 0.9659.