Find the Exact Value cos(-(5pi)/4)

Problem

cos(−(5*π)/4)

Solution

1. Apply the even-odd identity for the cosine function, which states that cos(−θ)=cos(θ)

cos(−(5*π)/4)=cos((5*π)/4)

2. Identify the reference angle by determining the position of (5*π)/4 on the unit circle.

(5*π)/4=π+π/4

3. Determine the quadrant and the sign of the cosine function. Since (5*π)/4 is in Quadrant III, the cosine value is negative.

cos((5*π)/4)=−cos(π/4)

4. Substitute the known value for the cosine of the reference angle π/4

cos(π/4)=√(,2)/2

5. Combine the results to find the final exact value.

cos(−(5*π)/4)=−√(,2)/2

Final Answer

cos(−(5*π)/4)=−√(,2)/2

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