Find the Exact Value sec(-2pi)

Problem

sec(−2*π)

Solution

1. Identify the periodicity of the secant function. Since the secant function has a period of 2*π we can add 2*π to the argument without changing the value.

sec(−2*π)=sec(−2*π+2*π)

2. Simplify the argument of the function.

sec(0)

3. Apply the definition of secant in terms of the cosine function.

sec(0)=1/cos(0)

4. Evaluate the cosine of 0 On the unit circle, the xcoordinate at 0 radians is 1

cos(0)=1

5. Substitute the value back into the fraction to find the final result.

1/1=1

Final Answer

sec(−2*π)=1

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