Question

Why do we write that the inverse function of sin is:

Answer 1

\[\sin ^{-1}\]since the inverse function of sin isn't \[\frac{ 1 }{ \sin }\]

Answer 2

the exponent of \(-1\) means the inverse of the function under composition, not the inverse of the number under multiplication

Answer 3

with numbers, \(a^{-1}=\frac{1}{a}\) because
\[a\times a^{-1}=1\] and \(1\) is the identity under multiplication

Answer 4

the inverse of a function \(f^{-1}\) is the function that, when composed with \(f\) gives the identity function \(I(x)=x\)

Answer 5

that is,
\[f^{-1}\circ f=I\]

Answer 6

means give the angle that has x for its sin that's not really true when you go further into trigonometry.

Answer 7

"means give the angle that has x for its sin"*

Answer 8

the operation is composition, not multiplication, and the identity is the identity function, not the number 1

Answer 9

the notation itself has nothing to do with trigonometry, it is the notation used for all functions
for example if \(f(x)=2x-1\) then \(f^{-1}(x)=\frac{x+1}{2}\) not \(\frac{1}{2x-1}\)

Answer 10

if you really have trouble using sin^-1, use arcsin you will be well-understood