Evaluate cos((11pi)/6)

Problem

cos((11*π)/6)

Solution

1. Identify the angle's position on the unit circle. The angle (11*π)/6 is in the fourth quadrant because it is between (3*π)/2 and 2*π

2. Determine the reference angle. Subtract the angle from 2*π to find the reference angle in the first quadrant.

Reference Angle=2*π−(11*π)/6

Reference Angle=(12*π)/6−(11*π)/6=π/6

3. Apply the cosine property for the fourth quadrant. In the fourth quadrant, the cosine function is positive.

cos((11*π)/6)=cos(π/6)

4. Evaluate the trigonometric value for the reference angle. Using the unit circle or special triangles, find the value of cos(π/6)

cos(π/6)=√(,3)/2

Final Answer

cos((11*π)/6)=√(,3)/2

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