Question

How do you evaluate the expression `sec(-30)`?

Answer 1

`sec(-30˚) = 2/sqrt(3) = (2sqrt(3))/3`

Explanation:

First of all, I as one like to work with positive angles. Since positive angles, when drawn in standard position, are drawn counter clockwise and negative angles are drawn clockwise, we can always find an equivalent negative/positive angle.

We use the equation `|a| + |b| = 360` to find the equivalent angle, where `a` and `b` are equivalent positive-negative angles.

Let `-30˚` be `a`.

`|-30| + |b| =360`

`30 + b = 360`

`b = 330˚`

Now, our task is to find the value of `sec(330˚)`. We know that `sectheta = 1/costheta`, so:

`sec(330˚) = 1/cos(330˚)`

`330˚` has a reference angle of `30˚`. Also, cosine is positive in the fourth quadrant. So, `cos330˚ = sqrt(3)/2`.

`1/cos330 = 1/(sqrt(3)/2) = 2/sqrt(3)`

I would recommend rationalizing the denominator.

`sec330˚ = 2/sqrt(3) xx sqrt(3)/sqrt(3) = (2sqrt(3))/3`

Hopefully this helps!