Answer:
1/2
Explanation:
We can use the unit circle and reference angle to find the exact value of sin(-5pi/6).
Starting from the positive x-axis (θ=0), we can rotate clockwise by 5pi/6 radians to get to the terminal side of -5pi/6.
The reference angle is pi/6 radians, which is the angle between the terminal side and the x-axis if we rotate counterclockwise instead.
At this angle, sin is negative and equal to -1/2, since the opposite side has length 1 and the hypotenuse has length 2.
Since sin is an odd function, we have sin(-5pi/6) = -sin(5pi/6) = -(-1/2) = 1/2.
Therefore, the exact value of sin(-5pi/6) is 1/2.