Question

I can't seem to remember or find a reliable thread on this.. Does

arcsin(sin(x))=x?
and does
sin(arcsin(x))=x?

Answer 1

Not all the time because the range of arcsin is -pi/2to pi/2 so if x = 5pi/6, for example, arcsin(sin(5pi/6))=pi/6

Answer 2

My equation is actually
S = 58.3+32.5cos((Π(t))/6)
and I have to get "t" by itself

Answer 3

Basically I need to know how to get "t" out of cos(Πt/6). Would arccos(cos(Πt/6)) = Πt/6?

Answer 4

\[\frac{S-58.3}{32.5}=\cos \frac{pi}{6}t\]
\[\frac{pi t}{6}=\cos^{-1} (\frac{S-58.3}{32.5})\]
\[t=\frac{6\cos^{-1}( .0307692(S-58.3))}{pi}\]

Answer 5

Interesting, I tried that the first time on my own but did a simple test with the number 5,\[x=\cos(5)\] I got x = .283662 when I reversed it it wouldn't work..
\[y=\arccos(x)\] y ended up being 1.28319.
I now realize my calculator was in radians which I didn't even think about it.. needless to say I basically entered a degree but when I use Π/3 for example, it works fine. Sorry to waste your time, but thanks for the help anyways. At least I can solve this problem now.

Answer 6

yw