Understanding Trigonometry

Understanding Trigonometry

This animation plots sin, cos, and tan.  Tan is cool because it has asymptotes (loosely: straight lines that the equation approaches but never reaches – kind of like the Cooper situation).  This is because for angle a, tan a = opposite/adjacent = sin a / cos a … but WAIT!  cos a sometimes comes out to 0!  We see that in the graph whenever the cosine line touches the x-axis.  Well, as you probably recall from algebra, you can’t divide by 0.  The answer is just undefined.  So when cos a hits 0, you’ll see the tan line jump to a remote y coordinate – in other words, it appears again at the edge.

Tan is sexy like that.  Just wait til we get to secant, cosecant, cotangent, arcsine, arccosine, and arctangent!!!!

8 thoughts on “Understanding Trigonometry”

  1. Dear James, Any idea why your math programs won’t run for me? My laptop is new, full of bells and whistles, and except for Sine, Cosine, and Trig, everything else has been visible. (Maybe it senses my inner fear and mistrust for complex math?)

    1. Hi Mary Ellen,
      It’s very likely that it’s my program’s fault, and not your computer’s. Let’s start with browser. Which browser are you using, and which version? In order to debug my code, I’ll need to open the web page using the same browser as you and see if I can narrow down the issue. Thanks.

  2. Internet Explorer, version 8. I had some issues with 64-bit systems (which I think this is, on a brand-spanking new HP Pavillion that only weighs 3 lbs. with the battery, yeehaw!) so I reverted to the regular IE instead of the 64-bit. I get what looks like default settings on your page: a list down the left-hand side of the page with places for your settings (sine, curve, etc..) but only the categories are there. Nothing else happens.

  3. You’ve made some changes to this since first posted, yes? I love this one. First of all, I didn’t realize you had audio and it completes the hypnotic effect (throw in a subliminal message, get Maggie to watch it, and you’ll have free luscious meals on your table every day). The only part of this I might know how to do is the final pop-up. This is exquisite, Jim.

  4. @Mary Ellen: It looks like IE8 doesn’t support scalable vector graphics (SVG). I knew IE6 and 7 didn’t, but figured they’d get it right by now. There is a plugin you can install to add SVG capabilities to IE, but for some reason, my SVG experiment fails to load.

    The easiest thing to do would be to install Firefox, then visit my site, but you could try the SVG plugin if you want. Instructions follow.

    Visit the SVG Viewer test page which will prompt you to install it. After the installer runs, the page reloads and you should see an animation. Now you can try coming back to my site, but I don’t think it’s going to work still.

    I’ll do some more digging on this issue.

    —-

    @susan: No, I haven’t changed anything. I know what you mean about the music only coming in the second time around. I had that experience too, and I’m not sure what the root cause is. That’s another thing I’ll be looking into.

    And as far as the code goes, please feel free to view source. I try to write comments into my code which will make it somewhat understandable to others.

  5. Well, we have what may be an improvement: I can see Adobe’s animations, and yours come up as a blank screen. Firefox may well solve the problem. I’ll let you know, and please don’t make yourself crazy trying to find out why I can’t see it. Apparently I’m the only one. Bummed about my wonderful investment not being able to translate it, though. (Or gee, is that still a Microsoft problem??)

    Thanks for all the help!

  6. Glad FF worked for you to see the animation. I think the plugin I’m using for the music is a little flaky, as Susan has reported some issues as well. My upcoming scripts will utilize different audio plugins to see which works best for all.

    And yes, Adobe plugins and Firefox usually do play well together. You won’t need the SVG plugin for Firefox … just the flash player plugin will do, because FF supports SVG natively, but needs a plugin for flash, which is what I’m using for audio playback in this particular script.

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