Simplify sin((11pi)/6)

Problem

sin((11*π)/6)

Solution

1. Identify the position of the angle (11*π)/6 on the unit circle. Since 0≤(11*π)/6<2*π we see that the angle is in the fourth quadrant.

2. Determine the reference angle by subtracting the angle from 2*π

Reference Angle=2*π−(11*π)/6

Reference Angle=π/6

3. Apply the sine function to the reference angle. We know from the unit circle that:

sin(π/6)=1/2

4. Determine the sign of the result based on the quadrant. In the fourth quadrant, the sine value (ycoordinate) is negative.

sin((11*π)/6)=−sin(π/6)

sin((11*π)/6)=−1/2

Final Answer

sin((11*π)/6)=−1/2

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