Find the Exact Value cos(-(13pi)/3)

Problem

cos(−(13*π)/3)

Solution

1. Use the even-odd property of the cosine function, which states that cos(−θ)=cos(θ)

cos(−(13*π)/3)=cos((13*π)/3)

2. Find the coterminal angle within the interval [0,2*π) by subtracting multiples of 2*π

(13*π)/3=4*π+π/3

3. Simplify the expression since cos(θ+2*k*π)=cos(θ) for any integer k

cos(4*π+π/3)=cos(π/3)

4. Evaluate the exact value using the unit circle or special right triangles.

cos(π/3)=1/2

Final Answer

cos(−(13*π)/3)=1/2

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