Answer: C: -1/2 (x-coordinate) and A: - ∛3 / 2 (y-coordinate)
Explanation:
1) In the unit circle, the x and y - coordinates are the cosine and sine ratios, respectivle.
2) 600° corresponds to 600 - 360° = 240°.
3) 180° < 240° < 270° ⇒ the point is in the third quadrant.
Third quadrant ⇒ both x and y coordinates are negative, so D. cannot be a solution.
4) You can work with the supplementary angle to use notable angles:
240° - 180° = 60°
The sine and cosine of 60° are known:
sin 60° = ∛3 / 2, and cos 60° = 1/2.
5) In the unit circle the x-coordinate is the cosine of the angle, and the y-coordinate is the sine of the angle:
So, x = - 1/2 and y = - ∛3/2.
6) You can verify in a calculator; sin 240° = -0.866... and cos 240° = - 0.5.
Therefore, the answer is: A: - ∛3 / 2, for the y-coordinate, and C: - 1/2 for the x-coordinate.
