This may be a beginner question, but I fear I need to ask it. Often when using graphing calculators online (Graphing Calculator) you see $sin(x)$ which gives a sine wave.
Yet, if you do $sin(180/pi)$, for example, then you get a straight line. I know that this happens because of the obvious reason that the sine will be constant.
But when you have sine(x) that has a curving line, is that graphing all of the different values of $x$?
Thanks for the help.
The calculator assigns to every arbitrary real number $x$ a value $f(x)$ and uses this to generate the graph of each corresponding ordinate $f(x)$ at each point on the $x$-line. It's the tips of all the ordinates that is the curve.
Thus when you input $f(x)$ in the utility, it assumes that you want the graph of the mapping $x\mapsto f(x)$ as described above. Now even if you input a constant, which of course $\sin(\text{whatever})$ is, where $\text{whatever}$ is some constant, it assumes you're plotting $x\mapsto \sin(\text{whatever}),$ which remains the same ordinate value $\sin(\text{whatever})$ at all values of $x.$