Find the Exact Value sec(180)

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 definition.

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 expression by dividing 1 by −1

sec(180^∘)=1/(−1)

sec(180^∘)=−1

Final Answer

sec(180^∘)=−1

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