Find the Exact Value sec(7)

Problem

sec(7)

Solution

1. Identify the expression as the secant of a real number, where the argument 7 is measured in radians.

2. Recognize that 7 is not a standard multiple of π (such as π/6 π/4 π/3 or π/2, which are typically used to find exact values using radicals or integers.

3. Determine if the expression can be simplified using trigonometric identities or angle addition formulas. Since 7 is a prime integer and not a rational multiple of π it cannot be expressed in a simpler "exact" radical form.

4. State the value in its simplest exact form, which is the expression itself, or relate it to its reciprocal function, the cosine.

Final Answer

sec(7)=sec(7)

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