Simplify cos((11pi)/6)

Problem

cos((11*π)/6)

Solution

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

2. Determine the reference angle. In the fourth quadrant, the reference angle is calculated as 2*π−θ

2*π−(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 using the unit circle or special triangles.

cos(π/6)=√(,3)/2

Final Answer

cos((11*π)/6)=√(,3)/2

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