Question

The measure of angle θ is 600°. . The point (x, y) corresponding to θ on the unit circle is? (___,___). the options for inside parenthesis are . A.) -(3^(1/2))/2. B.)-1(2^(1/2))/2. C.)-1/2. D.) (3^(1/2))/2

Answer 1

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.

Answer 2

Angle ( Theta ) = 600° - 360° = 240°
The point corresponding to (Theta) on the unit circle is:
( x , y ) = $( \frac{-1}{2}, \frac{- \sqrt{3} }{2} )$
Answer: ( C, A )