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

Problem

sin((2*π)/3)

Solution

1. Identify the quadrant of the angle (2*π)/3 Since π/2<(2*π)/3<π the angle is in the second quadrant.

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

3. Calculate the reference angle θ′ The reference angle for an angle in the second quadrant is found using the formula π−θ

θ′=π−(2*π)/3

θ′=π/3

4. Apply the reference angle to the sine function.

sin((2*π)/3)=sin(π/3)

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

sin(π/3)=√(,3)/2

Final Answer

sin((2*π)/3)=√(,3)/2

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