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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