What about it? What is the question?
Recall that
and
for all
. So


For
, we expect both
and
(i.e. the sine and cosine of any angle that lies in the first quadrant must be positive). By definition of absolute value,
if
.
So we have

making H the answer.
C is always true, because the inequality reduces to x > y.
Based on the picture, PC = PD
The range of sin(x) is [-1,1].
No matter what the value of x,pi,pi/2,pi/4,pi/6,-pi/2,etc the value of sinx will always be between -1 and 1(both included)