Find the Exact Value cos((15pi)/4)

Problem

cos((15*π)/4)

Solution

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

(15*π)/4−2*π=(15*π)/4−(8*π)/4

(15*π)/4−(8*π)/4=(7*π)/4

2. Identify the quadrant for the angle (7*π)/4 Since (3*π)/2<(7*π)/4<2*π the angle is in Quadrant IV.

3. Determine the reference angle θ′ for an angle in Quadrant IV using the formula θ′=2*π−θ

θ′=2*π−(7*π)/4

θ′=π/4

4. Apply the cosine sign for Quadrant IV. In Quadrant IV, the cosine function is positive.

cos((15*π)/4)=cos(π/4)

5. Evaluate the exact value using the unit circle or special right triangles.

cos(π/4)=√(,2)/2

Final Answer

cos((15*π)/4)=√(,2)/2

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