Find the Exact Value cos((23pi)/6)

Problem

cos((23*π)/6)

Solution

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

(23*π)/6−2*π=(23*π)/6−(12*π)/6

(23*π)/6−(12*π)/6=(11*π)/6

2. Determine the quadrant of the angle (11*π)/6 Since (3*π)/2<(11*π)/6<2*π the angle lies in Quadrant IV.

3. Find the reference angle for an angle in Quadrant IV using the formula (θ_ref)=2*π−θ

2*π−(11*π)/6=π/6

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

cos((11*π)/6)=cos(π/6)

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

cos(π/6)=√(,3)/2

Final Answer

cos((23*π)/6)=√(,3)/2

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