How do you get $\alpha$ from $\tan{\alpha}$?
Hello,
I want to know how to obtain $\alpha$ from $\tan{\alpha}$. I mean, what is a formula (if there is one)?
I know that it is schemes where it written that if $\tan{\alpha} = 2$ then $\alpha=63.43 ^{\circ}$.
What is a formula from which we can solve for $\alpha$?
I am not only interested in how to get $\alpha$ from $\tan{ \alpha }$. I also want to know how get $\alpha$ from $\sin{\alpha}$ and $\cos{\alpha}$.
$\endgroup$ 23 Answers
$\begingroup$There is an inverse function called arctangent. As the tangent is not one to one ($\tan (x+\pi)=\tan x)$ you have to choose which value you will return. The usual choice is that $-\frac \pi 2 \lt \arctan x \lt \frac \pi 2$
$\endgroup$ 2 $\begingroup$For all $x\in\mathbb R$ and $\alpha\in]-\pi/2,\pi/2[$, $$x=\tan \alpha\iff \alpha=\arctan(x)$$ then $$\tan(\alpha)=2\iff \alpha=\arctan(2)$$
$\endgroup$ $\begingroup$if $\tan(\alpha)=2$ the we get $\alpha=\arctan(2)$ Sonnhard.
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