Question

Determine the intervals of continuity of f(x)= ln(sin(x))
I looked at the graph and I have no idea how to state the intervals.

Answer 1

The primary function is ln(...)
we can only take logs of positive numbers
now look at the sine curve only, and note where it lies above the x-axis

so the intervals would be
0 < x < 90° or 360° < x < 450° or 720° < x < 810° or ...

how about something like
360n < x < 360n+90 , for n being an integer

or , in radians

2πn < x < (2πn + π/2) for n ∈ I