Find the Exact Value cos(-(9pi)/4)

Problem

cos(−(9*π)/4)

Solution

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

cos(−(9*π)/4)=cos((9*π)/4)

2. Find a coterminal angle within the interval [0,2*π] by subtracting 2*π from the argument.

(9*π)/4−2*π=(9*π)/4−(8*π)/4

(9*π)/4−(8*π)/4=π/4

3. Identify the exact value of the cosine function at the reference angle π/4 using the unit circle or special right triangles.

cos(π/4)=√(,2)/2

Final Answer

cos(−(9*π)/4)=√(,2)/2

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