Find the Exact Value sin((13pi)/6)

Problem

sin((13*π)/6)

Solution

1. Find the coterminal angle by subtracting 2*π from the argument to bring it within the standard interval [0,2*π]

(13*π)/6−2*π=(13*π)/6−(12*π)/6

(13*π)/6−(12*π)/6=π/6

2. Apply the periodic property of the sine function, which states sin(θ+2*π*n)=sin(θ)

sin((13*π)/6)=sin(π/6)

3. 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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