Find the Exact Value sin((11pi)/6)

Problem

sin((11*π)/6)

Solution

1. Identify the position of the angle (11*π)/6 on the unit circle.

2. Determine the quadrant by comparing the angle to 2*π noting that (11*π)/6=2*π−π/6 which places the angle in Quadrant IV.

3. Find the reference angle by calculating the distance to the nearest x-axis: 2*π−(11*π)/6=π/6

4. Recall the sine value for the reference angle π/6 which is sin(π/6)=1/2

5. Apply the sign for Quadrant IV, where the y-coordinate (sine) is negative.

Final Answer

sin((11*π)/6)=−1/2

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