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

1 Answer
Oct 26, 2016

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!