Evaluate cos((5pi)/3)

Problem

cos((5*π)/3)

Solution

1. Identify the angle (5*π)/3 on the unit circle.

2. Determine the reference angle by subtracting the angle from 2*π since it is in the fourth quadrant.

Reference Angle=2*π−(5*π)/3

Reference Angle=π/3

3. Determine the sign of the cosine function in the fourth quadrant. In the fourth quadrant, the xcoordinate is positive, so cos(θ) is positive.

4. Evaluate the cosine of the reference angle.

cos(π/3)=1/2

5. Combine the sign and the value to find the final result.

cos((5*π)/3)=1/2

Final Answer

cos((5*π)/3)=1/2

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