Take a look at the applet: sine function
Above you see the graph of with in radians on . The solutions of are shown ( is a constant).
The solution of within is called the arcsine of : .
There (often) is another solution within a range of one period.
Due to the symmetry of the graph that other solution is .
Because of the period of all solutions of are given by :
with any integer.
The equation only has solutions if .
There are some values that are convenient to use:
and vice versa:
You should use these values if exact values are required.