why is arccos(cos(3/4 pi)) = 3/4 pi but arcsin(sin(3/4 pi)) = 1/4 pi?

Question

why can't I directly cancel out arcsin and sin?

Answer 1

 

The angle 3*pi/4 = 135 degrees lies in the 2nd quadrant

 

In the 2nd quadrant, the cosine is negative but sine is positive