Find the Exact Value cos(-(7pi)/4)

Problem

cos(−(7*π)/4)

Solution

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

cos(−(7*π)/4)=cos((7*π)/4)

2. Find a coterminal angle or identify the position on the unit circle. The angle (7*π)/4 is in the fourth quadrant.

(7*π)/4=2*π−π/4

3. Determine the reference angle for (7*π)/4 which is π/4

Reference Angle=π/4

4. Evaluate the cosine in the fourth quadrant. Since cosine is positive in the fourth quadrant, the value is equal to cos(π/4)

cos((7*π)/4)=√(,2)/2

Final Answer

cos(−(7*π)/4)=√(,2)/2

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