Why and how are these problems, which look very similar, are actually different?

Question

1) sin^-1(sin(pi/4))= pi/4
2) sin^-1(sin(9 pi/4))=sin ^-1(sin(pi/4+2pi))=sin ^-1(sin(pi/4))=pi/4
3) sin ^-1(sin(11 pi/4))=sin^-1(sin(3 pi/4))=sin^-1(sin(pi/4))= pi/4

Answer 1

The equations sin x and cos x repeat at each interval of 2pi (or 360 degrees).

Thus, sin pi/4 = sin 9pi/4 = sin 17pi/4, etc.

Additionally, sin pi/4 = sin 3pi/4, because sin x peaks at pi/2 and returns to 0 at pi.

Answer 2

yup..
try to solve these typs of probs..which will give u more speed and experience..
coz...if u get a question of any similar type like this....it will be easy for u...

All these are similar...but answer might be diffrnt slightly/..