The graphs of the inverse trigonometric functions arcsin(x), arccos(x) and arctan(x) can all be drawn by reflecting the graphs y = sin(x), y = cos(x) and y = tan(x) respectively in the line y = x as the following videos demonstrate.

Take note of the domains.

y = arcsin(x)

Inverse Trig. Functions : arcsin(x) : ExamSolutions - youtube Video

y=arccos(x)

Inverse Trig. Functions : arccos(x) : ExamSolutions - youtube Video

y=arctan(x)

Inverse Trig. Functions : arctan(x) : ExamSolutions - youtube Video