Find the Exact Value sec(2.5)

Problem

sec(2.5)

Solution

1. Identify the expression as the secant of a value in radians. Since 2.5 does not have a degree symbol, it is treated as 2.5 radians.

2. Recall the reciprocal identity for the secant function.

sec(θ)=1/cos(θ)

3. Substitute the given value into the identity.

sec(2.5)=1/cos(2.5)

4. Determine if the value can be simplified further. Since 2.5 is not a standard multiple of π (like π/6 π/4 or π/3, the exact value is expressed in terms of the cosine function.

Final Answer

sec(2.5)=1/cos(2.5)

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