Question

Let x=33/65 be the x-coordinate of the point P(x,y), where the terminal side of angle theta (in standard position) meets the unit circle. If P is in Quadrant IV, what is sin theta?

Answer 1

cos theta = adj / hyp = (33/65) / 1 = 33/65
sin^2 theta = 1 = cos^2 theta = 1 - (33/65)^2 = 3136/4225
sin theta = sqrt(3136 / 4225) = 56/65

Therefore, sin theta = -56/65  (4th quadrant)