Find the Exact Value sec(-2)

Problem

sec(−2)

Solution

1. Identify the parity of the secant function. The secant function is an even function, meaning sec(−θ)=sec(θ)

2. Apply the even function property to the given expression.

sec(−2)=sec(2)

3. Determine if the value can be simplified further. Since 2 is in radians and is not a standard reference angle (like π/6 π/4 or π/3, the exact value is expressed in terms of the function itself.

4. Relate to the cosine function if necessary. By definition, sec(θ)=1/cos(θ)

sec(2)=1/cos(2)

Final Answer

sec(−2)=sec(2)

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