# Math Help - negative exponents

1. ## negative exponents

What does a negative exponent in front of number mean?
Example: sin ^-1 (0.53)
This is a problem involving refraction of light through two mediums such as water and air applying Snell's Law.

2. Originally Posted by dwedel
What does a negative exponent in front of number mean?
Example: sin ^-1 (0.53)
This is a problem involving refraction of light through two mediums such as water and air applying Snell's Law.
In general, it means an inverse (or when dealing with numbers, a reciprocal).

In this particular example, though, $\sin^{-1}\!\left(0.53\right)=\arcsin\!\left(0.53\right)$. It must be emphasized that $\sin^{-1}\!\left(a\right)\neq\left(\sin\!\left(a\right)\r ight)^{-1}$.

Does this help??

3. Originally Posted by Chris L T521
In general, it means an inverse (or when dealing with numbers, a reciprocal).

In this particular example, though, $\sin^{-1}\!\left(0.53\right)=\arcsin\!\left(0.53\right)$. It must be emphasized that $\sin^{-1}\!\left(a\right)\neq\left(\sin\!\left(a\right)\r ight)^{-1}$.

Does this help??
In other words, if you had the equation $\sin^{-1}(0.53) = x$ (say), it is asking you what angle (x) would be needed to have

$\sin{x} = 0.53$ hold true.

4. Originally Posted by Chris L T521
In general, it means an inverse (or when dealing with numbers, a reciprocal).

In this particular example, though, $\sin^{-1}\!\left(0.53\right)=\arcsin\!\left(0.53\right)$. It must be emphasized that $\sin^{-1}\!\left(a\right)\neq\left(\sin\!\left(a\right)\r ight)^{-1}$.

Does this help??
Yes it does. Thanks. dwedel