Question

Let point (a,b) be on a unit circle.

Answer 1

(C) sin(-r) = -a

(D) sin(r) = -a

Explanation:

The unit circle definition allows us to extend the domain of sine and cosine to all real numbers. The process for determining the sine/cosine of any angle θ is as follows:

Starting from (1,0) move along the unit circle in the counterclockwise direction until the angle that is formed between your position, the origin, and the positive x-axis is equal to θ.

1. sin θ is equal to the y-coordinate of your point, and
2. cosθ is equal to the xxx-coordinate.

In the question, sin(-r) = -a and sin(r) = -a is equal to the x-coordinate, thus they are not correct.

An image is attached for reference.