Find the Exact Value cos((13pi)/4)

Problem

cos((13*π)/4)

Solution

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

(13*π)/4−2*π=(13*π)/4−(8*π)/4

(13*π)/4−(8*π)/4=(5*π)/4

2. Determine the reference angle for (5*π)/4 Since this angle is in the third quadrant, subtract π from the angle.

(θ_ref)=(5*π)/4−π

(θ_ref)=π/4

3. Determine the sign of the cosine function in the third quadrant. In the third quadrant, cosine values are negative.

cos((5*π)/4)=−cos(π/4)

4. Substitute the known value for cos(π/4) which is √(,2)/2

cos((5*π)/4)=−√(,2)/2

Final Answer

cos((13*π)/4)=−√(,2)/2

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