Question

Using the unit circle, determine the value of sin(–240°).

a) -√3/2
b) √3/2
c) -1/2
d) 1/2

Answer 1

The value of sin(–240°) using the unit circle is -1/2. This is because the angle -240° corresponds to the angle 240° in the unit circle, which lies in the third quadrant where the sine value is the negative y-coordinate of the point.

Step-by-step explanation:

To find the value of sin(−240°) using the unit circle, let's start by determining the reference angle for −240°. The angle −240° corresponds to 360° - 240° = 120° in the positive direction.

Now looking at the unit circle, an angle of 120° is found in the second quadrant, where the sine value is positive. But since our original angle is -240°, we are moving in the clockwise direction, which brings us to the third quadrant, where sine values are negative. The reference angle in the third quadrant with the same sine value as 120° is 240°.

In the third quadrant, the coordinates for the angle 240° are (-√3/2,-1/2). The sine function gives us the y-coordinate, which is -1/2. Therefore, sin(−240°) = -1/2.