what are the sub topics of trigonometry?

Here is a partial list from Wikipedia: 

Altern base


Angle


Angular distance


Angle excess


Chord (geometry)


Circle (also see List of circle topics)


Unit circle


Degree (angle)


Grad (angle)


Hypotenuse


Opposites theorem


Ptolemy's theorem


Pythagorean theorem


Radian


Right angle


Thales' theorem


Trigonometric functions 





the list is extensive and subjective - any answer I give would be my opinion 

:)