Question 1161418
<pre>

{{{sec^(-1)((-2sqrt(3))/(3)))}}}

If an angle has a secant of

{{{(-2sqrt(3))/3}}} 

then it has a cosine which is its reciprocal

{{{-3/(2sqrt(3))}}} 

We rationalize the denominator:

{{{-3/(2sqrt(3))}}}{{{""*""}}}{{{sqrt(3)/sqrt(3)}}}

{{{-3sqrt(3)/(2*3)}}}

{{{-cross(3)sqrt(3)/(2*cross(3))}}}

{{{-sqrt(3)/2}}}

Angles that have this for their cosine are special angles that
we can find on the unit circle, in QII and QIII:

In degrees they are 150° and 210°

In radians they are 5&pi;/6 and 7&pi;/6

Edwin</pre>