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

Problem

cos((13*π)/6)

Solution

1. Identify the angle and determine if it is greater than one full rotation (2*π.

2. Find the coterminal angle by subtracting 2*π from the given angle to bring it within the range [0,2*π]

(13*π)/6−2*π=(13*π)/6−(12*π)/6

(13*π)/6−(12*π)/6=π/6

3. Evaluate the cosine of the coterminal angle using the unit circle or special right triangles.

cos((13*π)/6)=cos(π/6)

4. Determine the exact value of cos(π/6) which corresponds to 30

cos(π/6)=√(,3)/2

Final Answer

cos((13*π)/6)=√(,3)/2

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