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 
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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