Find the Exact Value sin((13pi)/3)

Problem

sin((13*π)/3)

Solution

1. Identify the angle and determine its position by finding a coterminal angle within the interval [0,2*π)

2. Subtract multiples of 2*π (which is (6*π)/3 from the given angle.

(13*π)/3−2*π=(13*π)/3−(6*π)/3=(7*π)/3

3. Subtract another 2*π to bring the angle within the standard range.

(7*π)/3−(6*π)/3=π/3

4. Evaluate the sine of the coterminal angle π/3 using the unit circle or special right triangles.

sin(π/3)=√(,3)/2

Final Answer

sin((13*π)/3)=√(,3)/2

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