Find the Exact Value sec(180 degrees )

Problem

sec(180)

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 of 180 into the expression.

sec(180)=1/cos(180)

3. Determine the value of cos(180) using the unit circle, where the coordinates at 180 are (−1,0)

cos(180)=−1

4. Simplify the fraction by substituting the value of the cosine.

sec(180)=1/(−1)

5. Calculate the final result.

sec(180)=−1

Final Answer

sec(180)=−1

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