Find the Exact Value cos(5/3*pi)

Problem

cos((5*π)/3)

Solution

1. Identify the angle in terms of its position on the unit circle. The angle (5*π)/3 is in the fourth quadrant because (3*π)/3<(5*π)/3<(6*π)/3

2. Determine the reference angle by subtracting the angle from 2*π

(θ_ref)=2*π−(5*π)/3

3. Simplify the reference angle calculation.

(θ_ref)=(6*π)/3−(5*π)/3=π/3

4. Apply the cosine property for the fourth quadrant. In the fourth quadrant, the cosine of an angle 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((5*π)/3)=1/2

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