Answer:
-1/2
Explanation:
You want to know the exact value of sin(-5π/6).
Reference angle
The reference angle is the smallest angle its terminal side makes with the x-axis. The angle -5π/6 is a 3rd-quadrant angle, whose reference angle is ...
-5π/6 +π = π/6
Trig function signs
You know that the signs of the sine and cosine trig functions are negative in the 3rd quadrant. Since you have memorized the short table of trig functions (first attachment), you know the value you're looking for is ...
sin(-5π/6) = -sin(π/6) = -1/2
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Additional comment
The second attachment shows the functions that are positive in the different quadrants. The ones not listed are negative.
The third attachment shows the coordinates on the unit circle as (cos, sin). The angle 7π/6 is the same as the angle -5π/6.
The fourth attachment shows you can put your calculator in radian mode and have it tell you the answer.