angles in trigonometry

You will get something like sin(an angle)= a number from the figure, and then you take the inverse of it.

Example: 

$\tan x = \dfrac{3}{2}\\ x = \tan^{-1}\dfrac{3}{2}\approx56.3^{\circ}$Last step is done by calculator.

Even this one!!:

$\sin x =\dfrac{1-\sqrt5}{2}\\ x = \sin^{-1}\dfrac{1-\sqrt5}{2}\approx 321.8^{\circ}$