Find the Exact Value 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)>0

4. Evaluate the cosine of the reference angle π/3 using known trigonometric values.

cos(π/3)=1/2

5. Apply the sign to the result. Since the cosine is positive in the fourth quadrant, the value remains positive.

Final Answer

cos((5*π)/3)=1/2

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