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Discussion: All Tools in Trigonometry on Sketchpad
Topic: Using Sketchpad to illustrate coterminal angles


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Subject:   RE: Using Sketchpad to illustrate coterminal angles
Author: Lillian
Date: Mar 12 2008
Nate,
Thanks for your (Rob's) trick.  I used it, along with LFS's idea about changing
the color as the angle goes around the circle.

I made a unit circle and a small "driver" circle, measured an arc angle on it,
multiplied that angle by 1000, marked that angle, then rotated the angle on my
unit circle by the marked angle.

Then, I animated the point (using an action button) on the smaller circle (at
the very slow speed of 0.0001).  I also put an action button to make the point
on the driver circle spin counterclockwise.

I display the unit circle and the marked angle, so that as the angle goes
around, the radian measure goes from 0 to 2000pi.

Finally, I put a "lap counter" on -- I divided the angle measure by 2pi
radians, and truncated the output.

To make the sketch beautiful, I traced the point, and set the point's color to
change parametrically based on the lap counter.  I set it to change
bidirectionally, with a "period" of 5.

I think I could post the sketch somewhere on this site, if people would like
it.

Lillian

On Mar 10 2008, NateB wrote:
> Lillian,
Here is a trick that my friend Rob Rumppe showed me.
> Create two points A and B on a circle with center C.  Measure the
> angle ACB.  Now create a measurement and multiply measure of angle
> ACB by (for example) 10.  Then "mark" the new (bigger) angle.  Now
> rotate point B by the marked angle around center C.  The transformed
> (rotated) angle will be able to get around the circle five times as
> B goes to pi.

I used this trick (but only to get to 2pi) in a
> circular trig sketch which can be found on this site:
> http://nateburchell.googlepages.com/index.html

I hope that this
> helps

Nate Burchell


On Mar 10 2008, Lillian wrote:
> Does
> anyone know if there's a way to illustrate angles with measures
>
> greater than 2pi using Sketchpad.  I'd love be able to draw a unit
> > circle, put a point on the unit circle, animate it, and display
> the
> radian measure of the arc formed as the point goes around the
> > circle, and have it not start over at 0 every time the point goes
> > around the circle.

Thanks,
Lillian

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