Find the Exact Value sec(33)

Problem

sec(33^∘)

Solution

1. Identify the expression as the secant of an angle measured in degrees, sec(33^∘)

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

3. Recognize that 33^∘ is not a standard reference angle (like 30^∘ 45^∘ or 60^∘.

4. Determine if the angle can be expressed as a sum or difference of standard angles. Since 33^∘ cannot be easily simplified into standard radicals using basic sum, difference, half-angle, or multiple-angle formulas without resulting in nested radicals or complex expressions, the exact value is typically represented in its trigonometric form.

5. Conclude that the exact value is sec(33^∘)

Final Answer

sec(33^∘)=sec(33^∘)

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