Find the Exact Value sec(2pi)

Problem

sec(2*π)

Solution

1. Identify the definition of the secant function in terms of the cosine function.

sec(θ)=1/cos(θ)

2. Substitute the given angle 2*π into the definition.

sec(2*π)=1/cos(2*π)

3. Determine the value of cos(2*π) using the unit circle. Since 2*π is a full rotation, it corresponds to the point (1,0)

cos(2*π)=1

4. Simplify the expression by dividing.

sec(2*π)=1/1

sec(2*π)=1

Final Answer

sec(2*π)=1

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