Find the Exact Value sin((-5pi)/6)

Problem

sin(−(5*π)/6)

Solution

1. Identify the angle in the unit circle. The angle −(5*π)/6 is measured clockwise from the positive x-axis.

2. Find the coterminal angle in the interval [0,2*π) by adding 2*π

θ=−(5*π)/6+(12*π)/6

θ=(7*π)/6

3. Determine the quadrant. The angle (7*π)/6 is in Quadrant III, where the sine function is negative.

4. Find the reference angle θ′

θ′=(7*π)/6−π

θ′=π/6

5. Apply the sine value for the reference angle. We know sin(π/6)=1/2

6. Assign the correct sign based on the quadrant. Since the angle is in Quadrant III, the value is negative.

sin(−(5*π)/6)=−1/2

Final Answer

sin(−(5*π)/6)=−1/2

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