For any angle θ in standard position, let P = (x, y) be the point on the terminal side of θ that is also on the circle x² + y² = r².

Question

Then, sin θ = ____ and cos θ = ____.

Answer 1

With a right triangle transcribed in a unit circle centered at the origin, per the Pythagorean theorem, x² + y² = r² . Since sinθ is the length of the side opposite θ divided by the hypotenuse and cosθ is the length of the side adjacent θ divided by the hypotenuse, sinθ = y/r and cosθ = x/r.