My professor taught us to solve few questions of sine by doing this. I don't understand what he did to get the answer. I can get the answer without doing any steps but I need to understand how he has done it.

Question:

sin(11pi/2)

= sin (3pi/2 + 8pi/2)

= sin (3pi/2 + 4pi)

= sin (3pi/2) <--- i don't know why 4pi just disappears.

= -1

Can I also get a different example with cosine and a negative sign so I can understand better. Thanks.