Help Determining (Dis)Continuity of a Trig Function

[vitaly]

I'm having problems finding whether or not a trig function is discontinuous or continuous. Besides graphing, I don't understand how you can tell. How do you know if a trig function is continuous or not, for the 6 basic functions?

 

[quantumdude]

You know that sin(x) and cos(x) are continuous, right? Well, the other trig functions are just made from sines and cosines. For example tan(x) is just sin(x) over cos(x). So tan(x) is going to be discontinuous whenever its denominator is zero. You can similarly analyze the other trig functions.