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

Problem

cos((7*π)/4)

Solution

1. Identify the quadrant of the angle (7*π)/4 Since (3*π)/2<(7*π)/4<2*π the angle lies in Quadrant IV.

2. Determine the reference angle (θ_r*e*ƒ) by subtracting the angle from 2*π

(θ_r*e*ƒ)=2*π−(7*π)/4

(θ_r*e*ƒ)=π/4

3. Apply the sign rule for the cosine function. In Quadrant IV, the cosine of an angle is positive.

cos((7*π)/4)=cos(π/4)

4. Evaluate the exact value of the cosine for the reference angle π/4

cos(π/4)=√(,2)/2

Final Answer

cos((7*π)/4)=√(,2)/2

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