Find the Exact Value sec(55)

Problem

sec(55^∘)

Solution

1. Identify the expression as the secant of an angle measured in degrees, sec(55^∘)

2. Relate the secant function to the cosine function using the reciprocal identity sec(θ)=1/cos(θ)

3. Determine if 55^∘ is a standard reference angle (like 0^∘,30^∘,45^∘,60^∘,90^∘. Since it is not, the exact value cannot be simplified into basic radicals or integers without using sum/difference formulas or half-angle identities that would result in a more complex nested radical expression.

4. Express the exact value in its simplest trigonometric form or in terms of its reciprocal.

Final Answer

sec(55^∘)=1/cos(55^∘)

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