True/false Revised?

Question

Is this right ? This is with respect to differentiation.

A.) sin[sin^-1 (-1)] = - 1

B.) sin^-1[sin(3pie/2)]=(3pie/2)

if not why not, because my calculator says its true.

A.) 0 = -1
B.) arcsin(sin^1(-1)))= 4,71238898
0=4,71238898

a bit confused?

Answer 1

Yes, the function and its inverse will cancel each other out. So, A & B (the top set) are true.

I don't quite understand what you have written in the second set.

Answer 2

arcsin(-1) = 3pi/2 , ( or -pi/2 )
sin (3pi/2) = sin(-pi/2) = -1

if you get 0 = -1, you are doing something wrong
is sin^-1 the same as arcsin ?, do you have the calculator in radius mode and stays it in radius mode ?
4,71238898 looks like 3/2 pi
is the - sign still before the 1 when you calculate arcsin(-1) I bet it is not.

Answer 3

1.sin[sin^-1(-1)]
=sin[sin^-1(sin270)]]
=sin 270 =-1
so true

2.sin^-1[sin3pi/2)]
=sin^-1(3pi/2)
=3pi/2 so true