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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