On Wed, Sep 18, 2024 at 8:12 AM Alan Grayson <[email protected]> wrote:
> > > On Wednesday, September 18, 2024 at 5:40:42 AM UTC-6 John Clark wrote: > > On Wed, Sep 18, 2024 at 1:16 AM Alan Grayson <[email protected]> wrote: > > *I'll get back to you on this. I was thinking, as x increases positively > or negatively, the y values (angles) repeat multiple times, making the > function many-to-one. In this case, we're mapping all the real numbers, to > a subset of the y-axis. Am I mistaken? AG * > > > *Arctan(1) = the angle whose tangent = 1. Isn't this angle 90 deg or > pi/2? So your plot seems wrong, but it's what is on the Internet. AG * > > > *That's wrong. Arctan(1) = pi/4, which is what the plot indicates. But I > still think the plot keeps repeating as x increases or decreases. AG* > > [image: image.png] > > > *1) **The range of the Arctangent function is the interval (-π/2,π/2) and > its range is all the real numbers.* > > *2) By dividing by π, the range scales to (-1/2, 1/2).* > > *3) Adding 1/2 shifts the range to (0,1) * > > *4) Thus for every real number x there is a unique number y between zero > and one that corresponds to it, and that number is Y=1/2 + 1/π Arctan(x) . > As I said before, the domain is all the real numbers and the range is (0,1)* > > > > *> Yes, but initially you were seeking a 1-1 function, but this one is > many-to-one. AG * > > FOR DARWIN'S SAKE! I GIVE UP! John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis> ugi -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAJPayv18HvVkAeDx1yvE1UM_K%2B4EvhqBDcXoA96V-h%3DpctxVuw%40mail.gmail.com.
