Find the Exact Value sec(4)

Problem

sec(4)

Solution

1. Identify the expression as the secant of 4 radians.

2. Determine if the angle is a standard value. Since 4 is not a multiple of π or a common reference angle (like π/6 π/4 or π/3, it cannot be simplified into a simpler radical or rational form.

3. Recognize that "exact value" in this context refers to the expression itself, as there are no algebraic identities or unit circle properties that reduce sec(4) further without using decimal approximations.

4. Express the result in terms of the reciprocal identity if desired, though sec(4) is already an exact representation.

Final Answer

sec(4)=sec(4)

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