File talk:Sine and Cosine fundamental relationship to Circle (and Helix).gif

Wow. This is excellent. Thank you for making it! --Hamsterlopithecus (talk) 00:19, 12 November 2008 (UTC)[reply]

Yeah, great work! Ehamberg (talk) 18:10, 20 November 2008 (UTC)[reply]

Glad to know you all like it. I know it would have helped me out a lot when I was first learning trig.--Tdadamemd (talk) 23:15, 12 December 2008 (UTC)[reply]

Very excellent visual portrayal of trig. Helped a lot thanks. WinterSpw (talk) 06:59, 14 January 2009 (UTC)[reply]

This image rocks, and you did it in powerpoint too. Wow. —Preceding unsigned comment added by 24.10.189.226 (talk) 05:03, 26 July 2009 (UTC)[reply]

You're very welcome, you all. Powerpoint was actually very easy to work with.

I distinctly remember being back in JrHigh when my math teacher, Gretchen V., spent the first minutes of class drawing on the chalkboard. She drew this graph with this curvy line and then she stepped back and told us it was a Sine Wave. I had absolutely no idea where it came from or what significance it had. It wasn't until I was a sophomore or junior in college when I was sitting in an electrical engineering class talking about phasors when all of a sudden the light bulb clicked on. It dawned on me that the sine wave was a projection of a helix. I did a sketch of that 3-D circle-sinewave-helix thing on the back of one of my class papers. That was a big day for me, lifting the veil of ignorance by an inch or so.

If only we had Wikipedia back then. Ha! --Tdadamemd (talk • contribs) 00:23, 24 January 2010

Thank you!!!! —Preceding unsigned comment added by 147.222.218.218 (talk) 18:56, 17 March 2011 (UTC)[reply]

My pleasure. Glad to have another satisfied customer. Mind if I call you '147.' for short? You can call me Tda, and we'll be on a first name basis. Ha!--Tdadamemd (talk) 09:32, 26 May 2011 (UTC)[reply]

How is this Euler's forumla?[edit]

This is a good explanation of sine and cosine, but the jump to Euler's formula is not really explained. I would leave that part out, unless you can explain how a helix becomes an exponential.

asmeurer (talk | contribs) 21:11, 2 October 2011 (UTC)[reply]

I didn't see your comment until today. Sorry for the long delay.

How's this Euler's formula? Please recognize the limited nature of this graphic. It is only a visual explanation of sine and cosine, given in under 2 minutes. What you appear to want is an explanation of Euler's formula. All this graphic is intended to offer is the geometric relationship of sine and cosine in 2-D to the circle, and then in 3-D to Euler's formula. There is only so much you can do in < 2 minutes.

It might also help if you think back to a time when certain people were only comfortable in talking about sine & cosine in terms of right triangles. These folks would freak when that relationship was extended to the circle. They resisted taking the mental leap involved in sweeping the angle in-plane through time. You are totally comfortable in that geometry. But your resistance is in taking that sweep through time out into the orthogonal direction, yet the geometry fits perfectly.

I do not know if Euler himself was able to make this mental visualization of the 3-D geometry inherent in his own formula. I mean, if he did then I would expect that he would have scribbled a sketch of the helix and that drawing would be just as famous as his equation. Euler may have only understood it in terms of a series of exponentials, which seems to be the explanation you are looking for. So you might take comfort in the idea that you're in excellent company!--Tdadamemd (talk) 15:09, 27 March 2012 (UTC)[reply]