Find the Exact Value sec((11pi)/3)

Problem

sec((11*π)/3)

Solution

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

(11*π)/3−2*π=(11*π)/3−(6*π)/3

(5*π)/3

2. Identify the reference angle for (5*π)/3 in the fourth quadrant.

2*π−(5*π)/3=π/3

3. Determine the sign of the secant function in the fourth quadrant.

secant is positive in Quadrant IV

4. Apply the reciprocal identity for secant.

sec((5*π)/3)=1/cos((5*π)/3)

5. Evaluate the cosine of the reference angle.

cos(π/3)=1/2

6. Calculate the final value by taking the reciprocal.

1/(1/2)=2

Final Answer

sec((11*π)/3)=2

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