expression

**samtheman17** · October 24th 2009, 11:32 AM

Find an expression for :

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

in terms of x

**adkinsjr** · October 24th 2009, 12:34 PM

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
$tan(\theta)=\frac{3}{x}$

$csc^2(Arctan(\frac{3}{x}))=1+\frac{1}{\frac{9}{x^2 }}=1+\frac{x^2}{9}$

**adkinsjr** · October 24th 2009, 12:42 PM

Note, I edited my original post because I messed up on the final line. So if you already looked at it, look again. It's fixed now. That should be the expression you're looking for.

- BTW, this kind of question probably should have been posted in the trignometry section, since these are inverse trig functions.

**samtheman17** · October 24th 2009, 01:20 PM

thank you! makes so much sense now

Thread: expression

LinkBack

Thread Tools

Display

expression

Similar Math Help Forum Discussions

Create sum expression from algebraic expression

Write the trigonometric expression as an algebraic expression in U

first expression of the second

An expression for a sum

DNF expression HELP!

Search Tags