Simplify sec(-pi)

Problem

sec(−π)

Solution

1. Identify the parity of the secant function. Since secant is the reciprocal of the cosine function, and cosine is an even function, sec(−x)=sec(x)

sec(−π)=sec(π)

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

sec(π)=1/cos(π)

3. Evaluate the cosine of π using the unit circle. At π radians (180, the xcoordinate is −1

cos(π)=−1

4. Substitute the value of cos(π) back into the expression to find the final result.

1/(−1)=−1

Final Answer

sec(−π)=−1

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