Question

How do I find the value of sec 330?

Answer 1

`sec(330º) = 2sqrt3/3`

Explanation:

Remember that `secx = 1/cosx`

So
`sec330º = 1/cos(330º)`

Remember that `cos(a-b) = cos(a)cos(b) + sin(a)sin(b)` and that `330º = 360º - 30º`, so

`cos(330º) = cos(360º - 30º) = cos(360º)cos(30º) + sin(360º)sin(30º)`

The cosine, sine, tangent and secant of 360º equal the cosine, sine, tangent and secant of 0º respectively. We know that `sin0º` is 0, and that `cos0º = 1` so

`cos(330º) = 1*cos(30º) + 0*sin(30º)`
`cos(330º) = sqrt3/2`

So

`sec(330º) = 2/sqrt3`

Rationalizing,

`sec(330º) = 2sqrt3/3`