solve the equation sin x=0.2 on the interval 0 is less than or equal to x is than (2pi)
$\displaystyle \sin(x) = \frac{1}{5} $
On way to solve this is to write:
$\displaystyle x = \arcsin(\frac{1}{5}) $, and simplify plug it into your calculator.
Another way is to consider a triangle. If you take the sin of an angle in a triangle, it gives the ratio of the length of the side opposite that angle and the hypotenuse.
Hence the hypotenuse of our triangle is 5, and the opposite side from angle x is 1. From pythagorus we calculate that the side adjacent to the angle x is $\displaystyle 2\sqrt{6} $
Now you know all lengths, you can work out the angle using the cosine rule.