Evaluate. Write your answer in simplified, rationalized form. Do not round.

Question

sec
​𝜋
6

Answer 1

Using the identity sec(x) = 1/cos(x), we can write:

sec(π/6) = 1/cos(π/6)

Since cos(π/6) = √3/2 (from the unit circle or trigonometric ratios), we can substitute:

sec(π/6) = 1/(√3/2)

To rationalize the denominator, we can multiply numerator and denominator by the conjugate of the denominator:

sec(π/6) = 1/(√3/2) * (√3/2)/(√3/2)

sec(π/6) = 2/√3

This is the simplified, rationalized form of sec(π/6).