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

Problem

sin((2*π)/3)

Solution

1. Identify the reference angle by determining how far the angle (2*π)/3 is from the x-axis.

Reference Angle=π−(2*π)/3=π/3

2. Determine the quadrant in which the angle (2*π)/3 lies. Since π/2<(2*π)/3<π the angle is in Quadrant II.

3. Apply the sign rule for the sine function. In Quadrant II, the sine of an angle is positive.

sin((2*π)/3)=sin(π/3)

4. Evaluate the sine of the reference angle using the unit circle or special right triangles.

sin(π/3)=√(,3)/2

Final Answer

sin((2*π)/3)=√(,3)/2

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