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

Problem

cos(−(11*π)/6)

Solution

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

cos(−(11*π)/6)=cos((11*π)/6)

2. Find the reference angle by determining how far the angle is from the nearest multiple of π Since (11*π)/6 is in the fourth quadrant, the reference angle is 2*π−(11*π)/6

Reference Angle=(12*π)/6−(11*π)/6=π/6

3. Determine the sign of the cosine function in the fourth quadrant. Since cosine is positive in the fourth quadrant, the value remains positive.

cos((11*π)/6)=cos(π/6)

4. Evaluate the exact value using the unit circle or special right triangles for the angle π/6

cos(π/6)=√(,3)/2

Final Answer

cos(−(11*π)/6)=√(,3)/2

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