Question

how do u know if sin^-1(x) is (sin(x))^-1 or 1/sinx = csc(x)?

Answer 1

the -1 power indicates the inverse function.

as far as i know, only american books use this confusing notation. it is always better to write \(\arcsin x\) for the inverse of \(\sin x\).

Answer 2

the exponent (-1) is reserved for the inverse of a function. sin^-1(x) is always the arcsin x (the inverse of sin x). if the reciprocal is intended, then it will be written \[\huge \left( \sin x \right)^{-1}\]

Answer 3

thanks. whats if its sin^-2(x)? is sin^10(x)=(sin(x))^10?

Answer 4

good point. it is a convention:
\[ \large \sin^nx=(\sin x)^n \]
ergo the confution.

Answer 5

\[\huge \sin^{-2}x=\frac{ 1 }{ \sin^2 x }\]. such notation sin^(-n) x is avoided because of the different interpretations it brings

Answer 6

so only true for n