Question

How do you find the value of `sec((7pi)/6)`?

Answer 1

`2/sqrt3 = - (2sqrt3)/3`

Explanation:

`sec ((7pi)/6) = 1/(cos ((7pi)/6)`
First, find `cos ((7pi)/6)`
The trig unit circle, and trig table give -->
`cos ((7pi)/6) = cos (pi/6 + pi) = - cos (pi/6) = - sqrt3/2`
Therefor:
`sec ((7pi)/6) = 1/(cos) = - 2/sqrt3 = - (2sqrt3)/3`