Find the Exact Value sec((17pi)/3)

Problem

sec((17*π)/3)

Solution

1. Find the coterminal angle by subtracting multiples of 2*π (which is (6*π)/3 until the angle is within the interval [0,2*π)

(17*π)/3−2*π=(11*π)/3

(11*π)/3−2*π=(5*π)/3

2. Determine the reference angle for (5*π)/3 which is located in the fourth quadrant.

(θ_ref)=2*π−(5*π)/3

(θ_ref)=π/3

3. Apply the reciprocal identity for secant.

sec((5*π)/3)=1/cos((5*π)/3)

4. Evaluate the cosine of the angle. In the fourth quadrant, cosine is positive.

cos((5*π)/3)=cos(π/3)

cos(π/3)=1/2

5. Calculate the final value by taking the reciprocal.

sec((17*π)/3)=1/(1/2)

sec((17*π)/3)=2

Final Answer

sec((17*π)/3)=2

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