Evaluate sin((7pi)/3)

Problem

sin((7*π)/3)

Solution

1. Find the coterminal angle by subtracting 2*π from the given angle to find an equivalent angle within the interval [0,2*π)

(7*π)/3−2*π=(7*π)/3−(6*π)/3

(7*π)/3−(6*π)/3=π/3

2. Identify the sine value for the reference angle π/3 (which is 60 using the unit circle or special right triangles.

sin(π/3)=√(,3)/2

3. Determine the sign based on the quadrant. Since π/3 is in the first quadrant, the sine value is positive.

sin((7*π)/3)=sin(π/3)

Final Answer

sin((7*π)/3)=√(,3)/2

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