Find the Exact Value sec((7pi)/3)

Problem

sec((7*π)/3)

Solution

1. Identify the periodicity of the secant function. Since sec(θ) has a period of 2*π we can subtract 2*π from the angle to find its coterminal equivalent within the interval [0,2*π)

2. Subtract the period from the angle:

(7*π)/3−2*π=(7*π)/3−(6*π)/3

(7*π)/3−(6*π)/3=π/3

3. Apply the reciprocal identity for secant:

sec(π/3)=1/cos(π/3)

4. Evaluate the cosine of the reference angle:

cos(π/3)=1/2

5. Calculate the final value by taking the reciprocal:

1/(1/2)=2

Final Answer

sec((7*π)/3)=2

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