How is $\sin x$ considered a function Yeah, it's a simple question, I forgot the exact reasoning behind it.
also would a one-to-one function be considered a function (obviously yes)? If it is then how come $\sin x$ is a function.
I'm very sure I'm getting confused with one to one function and multiple $y$ value vs 1 single $x$ value.
 A: $\sin(x)$ is a function because for any value of $x$, $\sin(x)$ gives one single value. Read more here.
A: Informally, a function is any rule which takes an  input and assigns a unique output.
Example: Let $x$ be the date, $f(x)$ be  the number of apples you ate that day. $f(x)$ is a function, because you cant eat both $2$ apples and $3$ apples, for example. 
Non-example: Let $x$ be the date, $f(x)$ a fruit you ate that day. Then if you had both an apple and an orange, $f(x)$ could be either one. It's ambiguous. This is fine as a 'relation' but it's not good enough to be a function. 
Sin(x) takes as input a real number (or angle) and outputs the unique $sine$ of that number.
A function is one-to-one if the rule outputs a different output for every input.
Example: Let $x$ be the current date. If since you've been born you've eaten one additional apple than the previous day, i.e. $f(x+1)=f(x)+1$ then you've eaten different numbers of apples on each day. So $f(x)$ is a function (as above) and it is also one-to-one.
Sin(x) is not one-to one, because $\sin(0^o)=\sin(180^o)$, for example.
A: $\sin(x)$ is a function, because -by definition- any value for $x$ produces only one value. A function can be one-to-one, but doesn't have to.
