Simplify sin((2pi)/3)

Problem

sin((2*π)/3)

Solution

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

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

(θ_ref)=π−(2*π)/3

(θ_ref)=π/3

3. Apply the property that the sine function is positive in the second quadrant.

sin((2*π)/3)=sin(π/3)

4. Evaluate the sine of the reference angle using the known values for special angles.

sin(π/3)=√(,3)/2

Final Answer

sin((2*π)/3)=√(,3)/2

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