Question

Given that cos0=0, find the coordinates of the point where the terminal side of 0 intersects the unit circle if 0 is an obtuse angle

Answer 1

On the unit circle the point for angle θ is (cosθ, sinθ). If cosθ = 0 then x = 0, so the possible intersection points are (0, 1) and (0, −1) (θ = π/2 or 3π/2).

If you insist θ is obtuse (90° < θ < 180°) the terminal side lies in quadrant II where y > 0, so the intersection would be (0, 1). Note: cosθ = 0 actually occurs at θ = 90° (a right angle) and 270°, so saying cosθ = 0 and θ is obtuse is inconsistent — only (0,1) and (0,−1) satisfy cosθ = 0.