On Wednesday, September 18, 2024 at 7:02:12 PM UTC-6 Alan Grayson wrote:
On Wednesday, September 18, 2024 at 6:50:53 PM UTC-6 Brent Meeker wrote: On 9/18/2024 5:19 AM, John Clark wrote: 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! Could'a told ya. Brent *Why are you so inclined to join the asshole club? I just made an error. Are you immune from that? AG* *I conjectured that Inflation caused the unobservable universe to come into existence, an original thought you ignore, but your inclination is to be petty. Too many physicists are revealed to be a'holes and I see no cure that. AG* -- 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/bf619990-6542-4f98-86e4-97d6ce955118n%40googlegroups.com.
