# expression

• Oct 24th 2009, 11:32 AM
samtheman17
expression
Find an expression for :

csc^2 (tan^-1 (3/x))

in terms of x
• Oct 24th 2009, 12:34 PM
Quote:

Originally Posted by samtheman17
Find an expression for :
csc^2 (tan^-1 (3/x))
in terms of x

I think this is what the problem looks like?
$csc^2(Arctan(\frac{3}{x}))$
Arctan is just one way of writing the inverse tangent function.

to solve this, let $\theta=Arctan(\frac{3}{x})$.
Therefore, $tan(\theta)=\frac{3}{x}$
and
$csc^2(Arctan(\frac{3}{x}))=csc^2(\theta)=1+cot^2(\ theta)=1+\frac{1}{tan^2(\theta)}$
So now you can write this in terms of
$tan(\theta)=\frac{3}{x}$

$csc^2(Arctan(\frac{3}{x}))=1+\frac{1}{\frac{9}{x^2 }}=1+\frac{x^2}{9}$
• Oct 24th 2009, 12:42 PM