What are the coordinates of a unit circle with angle 3π/4 ?

On a unit circle the radius is 1, so any point on the circle is written as (cos θ, sin θ). To answer this we just need cos(3π/4) and sin(3π/4).

3π/4 is 135°. That lands in the second quarter of the circle, where x is negative and y is positive. The reference angle is 180° − 135° = 45°, and for 45° both cosine and sine equal √2/2.

Putting the signs back: cos(3π/4) = −√2/2 and sin(3π/4) = +√2/2. So the coordinates are ( −√2/2 , √2/2 ). The pair with both values positive is the point for 45°, not 135°, and the pairs using √3/2 belong to 30° or 60° angles, so they cannot be right.