Find the Exact Value cos((11pi)/3)

Problem

cos((11*π)/3)

Solution

1. Find a coterminal angle within the standard interval [0,2*π] by subtracting multiples of 2*π

(11*π)/3−2*π=(11*π)/3−(6*π)/3

(5*π)/3

2. Determine the quadrant of the angle (5*π)/3 Since (3*π)/2<(5*π)/3<2*π the angle lies in Quadrant IV.

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

θ′=2*π−(5*π)/3

θ′=π/3

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

cos((5*π)/3)=cos(π/3)

5. Evaluate the cosine of the reference angle using known trigonometric values.

cos(π/3)=1/2

Final Answer

cos((11*π)/3)=1/2

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