# What methods are known for solving tan^2(x)=1000?

• Feb 5th 2013, 09:29 AM
Lambin
What methods are known for solving tan^2(x)=1000?
PROBLEM:
$\displaystyle tan^2(x)=1000$

ATTEMPT:
From what I can tell, simply taking the square root of tan(x) will not work; transcendental operators don't work exactly like algebraic operators? Do I have to transform $\displaystyle tan^2(x)$ into a different expression to solve for x, or is there another method I'm overlooking?
• Feb 5th 2013, 09:37 AM
Plato
Re: What methods are known for solving tan^2(x)=1000?
Quote:

Originally Posted by Lambin
PROBLEM:
$\displaystyle tan^2(x)=1000$
ATTEMPT:
From what I can tell, simply taking the square root of tan(x) will not work; transcendental operators don't work exactly like algebraic operators? Do I have to transform $\displaystyle tan^2(x)$ into a different expression to solve for x, or is there another method I'm overlooking?

There are two square roots of 1000: $\displaystyle \pm 10\sqrt{10}$.

Use the $\displaystyle \arctan$ function.