Find the Exact Value sin(2/3*pi)

Problem

sin(2/3*π)

Solution

1. Identify the angle 2/3*π on the unit circle. This angle is located in the second quadrant because π/2<2/3*π<π

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

Reference Angle=π−2/3*π

Reference Angle=1/3*π

3. Apply the sine function to the reference angle. The sine of π/3 (or 60 is a standard trigonometric value.

sin(π/3)=√(,3)/2

4. Determine the sign of the result based on the quadrant. In the second quadrant, the sine function is positive.

sin(2/3*π)=sin(π/3)

Final Answer

sin(2/3*π)=√(,3)/2

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