whats the limit of the sequence $a_n =[3+\cos(nπ/2)]/[2+\sin(nπ/2)] $ when $n\to \infty$

Question

$$\lim_{n\to\infty} a_n = \lim_{n\to\infty}\frac {3+\cos(n\pi/2)}{2+\sin(n\pi/2)} $$

I don't understand how to calculate trigonometric limits to infinity, therefore, I am lost.

Thanks for the tips. I understand what you want to say but i still don't know how i should present it on Paper.

Answer 1

HINT: Note that $a_{4n}=2$ and $a_{4n+2}=1$. What does this tell you about the limit of $a_n$ as $n\to\infty$?

Answer 2

Hint: When $n$ is odd, $\cos(nπ/2)=0$ and $\sin(nπ/2)=\pm1.$ When $n$ is even, the reverse case occurs.