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.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 rangescales to (-1/2, 1/2).* * 3) Adding 1/2 shifts the range to (0,1) * *4) Thus for every real numberx 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
John K Clark See what's on my new list at Extropolis <https://groups.google.com/g/extropolis>
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