You have the normal trigonometric functions cos, sin and tan. The invertion is more or less the same for all of these functions.
Let's use cosine for this example.
As you probably know you can use cosine to calculate the ratio and thereby the sides of either an adjecent catet or the hypotenuse.
I.E.:
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{78}}^\circ\right)} = {\frac{{\mathtt{3}}}{{\mathtt{x}}}}$$
3 being the lenght of the catet and x being the unknown hypotenuse.
Inverse trigonometric functions work the other way around, if you already know the ratio you can use the inverse trigonometrical functions to find the angle.
The functions are shown in calculators as either
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left(\right)}$$
or
$${acos}\left($$
If the ratio is for example 3.7 you would type $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\mathtt{3.7}}\right)}$$ in a calculator to get the angle.
Note however that you sometimes have to mark that you want the answer shown in degrees and not in radiuses.
