Simplify sin((13pi)/6)

Problem

sin((13*π)/6)

Solution

1. Identify the angle and determine if it is greater than one full revolution. Since 2*π=(12*π)/6 the angle (13*π)/6 is greater than 2*π

2. Find the coterminal angle by subtracting 2*π from the original angle to bring it within the interval [0,2*π)

(13*π)/6−2*π=(13*π)/6−(12*π)/6

(13*π)/6−(12*π)/6=π/6

3. Apply the periodic property of the sine function, which states sin(θ+2*π*k)=sin(θ) for any integer k

sin((13*π)/6)=sin(π/6)

4. Evaluate the sine of the reference angle π/6 (or 30 using the unit circle or special right triangles.

sin(π/6)=1/2

Final Answer

sin((13*π)/6)=1/2

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