Find the Exact Value sec(20)

Problem

sec(20^∘)

Solution

1. Identify the expression as the secant of an angle measured in degrees.

2. Recognize that 20^∘ is not one of the standard reference angles (like 0^∘ 30^∘ 45^∘ 60^∘ or 90^∘ for which exact values are typically memorized in basic trigonometry.

3. Relate the secant function to the cosine function using the reciprocal identity.

sec(20^∘)=1/cos(20^∘)

4. Determine if a closed-form algebraic expression exists. While cos(20^∘) can be expressed using radicals and complex numbers via the triple-angle formula cos(3*θ)=4*cos^3(θ)−3*cos(θ) the resulting value involves roots of non-real complex numbers (the irreducible case of the cubic equation).

5. Conclude that the simplest exact form is the expression itself or its reciprocal identity.

Final Answer

sec(20^∘)=1/cos(20^∘)

Want more problems? Check here!