Find the Exact Value sec((5pi)/3)

Problem

sec((5*π)/3)

Solution

1. Identify the reference angle for (5*π)/3 by determining its position on the unit circle. Since (5*π)/3 is in the fourth quadrant, the reference angle is 2*π−(5*π)/3=π/3

2. Apply the reciprocal identity for the secant function, which states that sec(θ)=1/cos(θ)

3. Determine the sign of the cosine function in the fourth quadrant. In the fourth quadrant, cos(θ) is positive.

4. Evaluate the cosine of the reference angle π/3

cos(π/3)=1/2

5. Calculate the secant value by taking the reciprocal of the cosine value.

sec((5*π)/3)=1/(1/2)=2

Final Answer

sec((5*π)/3)=2

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