Name and security of these non-invertible functions?
If I understood your question correctly, you want a message authentication code (MAC). The "hidden input" is usually called key and the "visible input" is just the message. The output of the MAC is called tag (or also MAC).

The main security goal for MACs is resistance against forgery: It should be computationally infeasible for an attacker who does not possess the key to obtain a valid tag for any message whose tag they have not observed before.

Common variants of that primitive include HMAC, CMAC, or Poly1305-AES, just to name a few.



Now, about your algorithm: Usually, homebuilt ad-hoc constructions are a very bad idea. Unfortunately, I did not find a trivial way to completely break yours during the few minutes I thought about it, even though I'm sure the mathematical properties of the sine function are highly useful to attack it. However, if you look at the examples I just linked, you will see that these are quite a bit more complicated than your proposal — and there is a reason for that. Many simple constructions suffer from unforeseen vulnerabilities once examined a bit more carefully: My favourite example is the "keyed hash" $\mathit{msg}\mapsto H(\mathit{key}\Vert \mathit{msg})$, where $H$ is a Merkle-Damgård hash such as MD5, SHA1 or SHA2. This suffers from a length extension attack and is thus not a secure MAC even it may seem so at first.

The bottom line is: Crypto is hard. Please use one of the well-established primitives from a well-established implementation if you have to protect anything of importance.