To use the unit circle to find the exact value of sin(330°), we can follow these steps:
Draw the unit circle with the positive x-axis as the initial side of the angle and counterclockwise as the rotation direction.
- Find the reference angle by subtracting the nearest multiple of 360°, which is 300°, from 330°:
330° - 300° = 30°
- Determine the quadrant in which the angle terminates. Since 330° is in the fourth quadrant, the sine function will be negative.
Identify the coordinates of the point on the unit circle that corresponds to the reference angle of 30°.
Since the reference angle is 30°, the corresponding point is located on the terminal side of the angle formed by rotating 30° counterclockwise from the positive x-axis. This point has coordinates of (cos(30°), sin(30°)), which are (√3/2, 1/2).
Use the sign of the trig function in the appropriate quadrant to determine the final value of sin(330°). Since 330° is in the fourth quadrant and the sine function is negative in the fourth quadrant, sin(330°) = -sin(30°) = -1/2.
Therefore, the exact value of sin(330°) is -1/2.