# Thread: working with inverse trig functions

1. ## working with inverse trig functions

Hey, all.

In another thread, someone was asking a question which involved solving this equation for x:

$\displaystyle \frac{\arctan{x}}{\arccos{x}}=\frac{\sqrt{1-x^2}}{1+x^2}$

How would one go about tackling something like that? Can it even be done?

Thoughts?

2. Originally Posted by hatsoff
Hey, all.

In another thread, someone was asking a question which involved solving this equation for x:

$\displaystyle \frac{\arctan{x}}{\arccos{x}}=\frac{\sqrt{1-x^2}}{1+x^2}$

How would one go about tackling something like that? Can it even be done?

Thoughts?
I don't think we can find an exact answer. We can approximate $\displaystyle x$, though.

One way [using calculus] would be to apply the Newton-Raphson Method: $\displaystyle x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$

where $\displaystyle f(x)=\sqrt{1-x^2}\cos^{-1}(x)-(1+x^2)\tan^{-1}(x)$

I hope this helps!

--Chris

3. Originally Posted by hatsoff
Hey, all.

In another thread, someone was asking a question which involved solving this equation for x:

$\displaystyle \frac{\arctan{x}}{\arccos{x}}=\frac{\sqrt{1-x^2}}{1+x^2}$

How would one go about tackling something like that? Can it even be done?