1. ## Find cot(x)

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

Anyone? Last question of the year.

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

$\displaystyle -2sinx = 1$

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

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

easy to get $\displaystyle cotx$ from this

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

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.

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

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

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

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

y = -1, r = 2

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

$\displaystyle x=\sqrt{3}$

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

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