Evaluate. Write your answer in simplified, rationalized form. Do not round.
sec
𝜋
6
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).