# How do you evaluate sec^-1(-2/sqrt3)?

Aug 18, 2016

150 degrees or 5$\pi$/3

#### Explanation:

sec$^ - 1$ means the angle whose secant is -2/$\sqrt{3}$
Which is the angle whose cosine is -sqrt3/2

Draw an equilateral triangle and cut in half.
The ratio of the sides of the right angle triangle are 1:2::$\sqrt{3}$

So the angle whose cosine is +$\sqrt{3}$/2 is 30 degrees or $\pi$/3

From the cosine graph the angle whose cosine is-$\sqrt{3}$/2 is 150 degrees or 5$\pi$/3