Find the Exact Value sec((13pi)/3)

Problem

sec((13*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

(13*π)/3−(6*π)/3=(7*π)/3

(7*π)/3−(6*π)/3=π/3

2. Apply the reciprocal identity for the secant function.

sec(π/3)=1/cos(π/3)

3. Evaluate the cosine of the reference angle π/3 (or 60.

cos(π/3)=1/2

4. Calculate the final value by taking the reciprocal.

1/(1/2)=2

Final Answer

sec((13*π)/3)=2

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