Find the Exact Value cos((14pi)/3)

Problem

cos((14*π)/3)

Solution

1. Find the coterminal angle by subtracting multiples of 2*π until the angle is within the interval [0,2*π)

2*π=(6*π)/3

(14*π)/3−(6*π)/3=(8*π)/3

(8*π)/3−(6*π)/3=(2*π)/3

2. Identify the reference angle for (2*π)/3 in the second quadrant.

π−(2*π)/3=π/3

3. Determine the sign of the cosine function in the second quadrant.

In Quadrant II, cosine is negative.

4. Evaluate the cosine of the reference angle and apply the negative sign.

cos(π/3)=1/2

cos((2*π)/3)=−1/2

Final Answer

cos((14*π)/3)=−1/2

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