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

Problem

sin((5*π)/6)

Solution

1. Identify the reference angle by determining how far the angle (5*π)/6 is from the nearest xaxis.

Reference Angle=π−(5*π)/6=π/6

2. Determine the quadrant of the angle (5*π)/6 Since π/2<(5*π)/6<π the angle lies in Quadrant II.

3. Determine the sign of the sine function in Quadrant II. In the second quadrant, the sine of an angle is positive.

sin((5*π)/6)=sin(π/6)

4. Evaluate the sine of the reference angle π/6 (or 30 using the unit circle or special right triangles.

sin(π/6)=1/2

Final Answer

sin((5*π)/6)=1/2

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