Question

Discuss the continuity of the cosine, cosecant and secant functions.

Answer 1

Function y $=$ f(x) is continuous at point x$=$ a if the following three conditions are satisfied :
i.) f(a) is defined ,
ii.) $\underset{x\to a}{lim}f\left(x\right)$ exists (i.e., is finite) ,
and
iii.) $\underset{x\to a}{lim}f\left(x\right)=f\left(a\right)$
We can also see the continuity by graph of function
$i)$ Cosine
Cosine is continuous function
$ii)$cosecant
Cosecant is discontinuous at $x=n\pi wherenisinteger$
$iii)$Secant
Secant is discontinuous at $x=\frac{n\pi }{2}wherenisinteger$