Which of $\sin^{-1}()$ and $\sin^{(-1)}()$ refers to $\arcsin(\sin(x)) = x$ and $\csc(x) = \frac{1}{\sin(x)}$?
Asked
Active
Viewed 84 times
0
-
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. – Community Jan 17 '24 at 15:06
-
2Welcome to Math.SE! ... This question has been asked numerous times here, so you are in good company. :) See, for instance, "What is the authoritative consensus on ambiguous notation of $\sin^{−1}()=\arcsin()$ vs. $\sin^{−1}()=\csc()$?". For more examples, look through the results of a site search for "arcsin csc". – Blue Jan 17 '24 at 15:17
-
1Your post doesn't mention calculus but $\sin^{(-1)}x$ could be construed as the $-1$-th derivative of $\sin x$, i.e. its "first" antiderivative. $\dfrac{d^n f(x)}{dx^n}\equiv f^{(n)}(x)$ is a fairly common notation. – user170231 Jan 17 '24 at 15:23
1 Answers
1
To the best of my knowledge, there is no agreed upon applicable universal convention.
So, if you are the reader, you have to try to guess the intent from the surrounding context.
If you are the writer, it is best to specify what convention that you are using. In the alternative, you can use the unambiguous arcsin$(x)~$ and $~\left[ ~\sin(x) ~\right]^{-1}.$
user2661923
- 42,303
- 3
- 21
- 46