1. ## Find cot(x)

Function: csc(x)=-2
find cot.

Anyone? Last question of the year.

2. Originally Posted by BeSweeet
csc(x)=-2
$
\frac{1}{sinx} = -2
$

$
-2sinx = 1
$

$
sinx = -\frac{1}{2}
$

$
sin^{-1}\left(-\frac{1}{2}\right) = -\frac{\pi}{6}
$

easy to get $cotx$ from this

since $cosx(-\frac{\pi}{6}) = -\frac{\sqrt{3}}{2}$
and $cotx$ is $\frac{adj}{hyp}$ then $cotx$ is just $
-\sqrt{3}$

3. Originally Posted by BeSweeet
Function: csc(x)=-2
find cot.

Anyone? Last question of the year.
Hi BeSweet,

Last question? Wow. Have a very merry Christmas.

$\csc x = \frac{1}{\sin x}=-2$

$\sin x = -\frac{1}{2}$

Use $r^2=x^2+y^2$ to find x.

$\sin x =\frac{y}{r}=-\frac{1}{2}$

y = -1, r = 2

$2^2=x^2+(-1)^2$

$x=\sqrt{3}$

$\tan x=\frac{y}{x}$

$\cot x = \frac{1}{\tan x}=\frac{x}{y}=\frac{\sqrt{3}}{-1}=-\sqrt{3}$