Question

Arcsec -(2sqrt3)/(3)

Answer 1

\(\bf sec^{-1}\left(-\cfrac{2\sqrt{3}}{3}\right)\qquad recall\quad sec(\theta)=\cfrac{1}{cos(\theta)}\implies cos(\theta)=\cfrac{1}{sec(\theta)}\quad\\ thus\\ \quad \\
sec^{-1}\left(-\cfrac{2\sqrt{3}}{3}\right)\implies sec(\theta)=\left(-\cfrac{2\sqrt{3}}{3}\right)\implies \cfrac{1}{\left(-\frac{2\sqrt{3}}{3}\right)} = cos(\theta)\\ \quad \\
-\cfrac{3}{2\sqrt{3}} = cos(\theta)\implies -\cfrac{3}{2\sqrt{3}} \cdot \cfrac{\sqrt{3}}{\sqrt{3}}= cos(\theta)\implies

-\cfrac{\cancel{3}\sqrt{3}}{\cancel{6}}= cos(\theta)\\ \quad \\
\cfrac{\sqrt{3}}{2}= cos(\theta)\)

Answer 2

\[\sec(x) = -\frac{2\sqrt{3}}{3}\]
sec = 1/cos
so
1/sec = cos
\[\cos(x) = -\frac{3}{2\sqrt{3}} = -\frac{3\sqrt{3}}{6} = -\frac{\sqrt{3}}{2}\]
using unit circle
x = 150 degrees

Answer 3

lol

Answer 4

negative for that matter \(\bf -\cfrac{\sqrt{3}}{2}= cos(\theta)\)