Question

Difference between negative exponent and inverse functions?

For example,
sine inverse: sin^-1(x)
or
1/(sin(x)) = (sin(x))^-1

Answer 1

the negative indice means to find the reciprocal of sin(x)

so given

\[\sin(x) = \frac{\sin(x)}{1}\]

then the reciprocal is

\[(\frac{\sin(x)}{1})^{-1} = \frac{1}{\sin(x)}\]

and for the inverse function

if

\[\sin(x) = \frac{a}{b}\]

the sin of an angle is equal to a ratio

then

\[x = \sin^{-1}(\frac{a}{b})\]

the angle is equal to the inverse sin of the ratio.

its the 2 way connection between and angle and a ratio.

hope it helps.