Answer
Cosine is a continuous function.
Work Step by Step
According to (6):
$\lim\limits_{\theta \to 0}sin~\theta = 0$
$\lim\limits_{\theta \to 0}cos~\theta = 1$
Choose any real number $a$
We can evaluate $\lim\limits_{h \to 0}cos(a+h)$:
$\lim\limits_{h \to 0}cos(a+h)$
$=\lim\limits_{h \to 0}~(cos~a~cos~h-sin~a~sin~h)$
$=[cos~a~(1)-sin~a~(0)]$
$= cos~a$
For all real numbers, $\lim\limits_{h \to 0}cos(a+h) = cos~a$
Therefore, cosine is continuous for all numbers.
Cosine is a continuous function.
