26.4k views
1 vote
On a unit circle, the ordered pair (x, y) represents the point where the terminal side of θ intersects the unit circle. If m<θ = 120*, what is the value of x in simplest form?

a. -1/2
b. 1/2
c. -√3/2
d. √3/2

User Westwick
by
7.2k points

1 Answer

5 votes

Final answer:

The value of x on a unit circle at an angle of 120° is -1/2, because it corresponds to the negative cosine of 60°, which lies in the second quadrant where the cosine values are negative.

Step-by-step explanation:

The student has asked about the value of the x-coordinate on a unit circle when the terminal side of an angle θ intersects the unit circle at an angle of 120°.

In trigonometry, the x-coordinate corresponds to the cosine of the angle, and the y-coordinate corresponds to the sine of the angle. For an angle of 120°, which lies in the second quadrant of the unit circle, the cosine is negative. The cosine of 120° is actually the cosine of 60° taken with a negative sign because 120° is supplementary to 60° (which is 180° - 120° = 60°).

Since the cosine of 60° is ½, the value of x at 120° will be negative ½. Thus, the correct answer to the question would be (a) -1/2.

User Heath Dutton
by
7.8k points