Question

Point P on the unit circle is given. What is the sine of the angle formed by a terminal ray that intersects the unit circle at thispoint

Answer 1

If P = (x,y) lies on the unit circle and the terminal ray meets the circle at P, then the angle θ satisfies cos θ = x and sin θ = y.

So the sine of the angle is the y‑coordinate of P. (E.g. if P = (√2/2, √2/2), sin θ = √2/2.)