Find the Exact Value sec(2)

Problem

sec(2)

Solution

1. Identify the expression as the secant of 2 radians.

2. Recognize that 2 is not a standard reference angle (like 0 π/6 π/4 π/3 or π/2 for which exact algebraic values involving radicals are typically derived in trigonometry.

3. Apply the reciprocal identity to express the secant function in terms of the cosine function.

sec(θ)=1/cos(θ)

4. Substitute the value 2 into the identity.

sec(2)=1/cos(2)

5. Conclude that since 2 is not a special angle, the most precise "exact value" is the expression itself or its reciprocal form.

Final Answer

sec(2)=1/cos(2)

Want more problems? Check here!