Find the Exact Value sec(-pi)

Problem

sec(−π)

Solution

1. Identify the property of the secant function for negative angles. Since secant is an even function, sec(−θ)=sec(θ)

sec(−π)=sec(π)

2. Relate the secant function to the cosine function using the reciprocal identity sec(x)=1/cos(x)

sec(π)=1/cos(π)

3. Determine the value of cos(π) using the unit circle. At an angle of π radians (180, the xcoordinate is −1

cos(π)=−1

4. Substitute the value of the cosine function back into the reciprocal expression to find the final result.

1/(−1)=−1

Final Answer

sec(−π)=−1

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