Find the Exact Value cos((11pi)/6)

Problem

cos((11*π)/6)

Solution

1. Identify the quadrant of the angle (11*π)/6 Since (11*π)/6 is between (3*π)/2 and 2*π the angle lies in Quadrant IV.

2. Determine the reference angle (θ_R) In Quadrant IV, the reference angle is calculated as 2*π−θ

(θ_R)=2*π−(11*π)/6

(θ_R)=π/6

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

cos((11*π)/6)=cos(π/6)

4. Evaluate the cosine of the reference angle using the unit circle or special triangles.

cos(π/6)=√(,3)/2

Final Answer

cos((11*π)/6)=√(,3)/2

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