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Going in Circles

You may have already noticed that when you drag the stick, the handle traces out a semi-circular arc. Here’s the picture again with the arc drawn in, and no more shadows. Feel free to drag the hypotenuse and check out the sine and cosine.


[Applet appears here for Java-capable browsers]

Of course, there’s no reason that we can’t swing the hypotenuse around in a complete circle (360 degrees).


[Applet appears here for Java-capable browsers]

If the length of the hypotenuse is exactly one unit, we call the circle that the end of the hypotenuse draws a unit circle. This will be important later.

Real World Alert! At this point, we have to abandon the shadows. Setting up a set of lights and walls to catch the shadows from both above and below is really difficult. In the great outdoors, we can’t do anything once the sun slips below the horizon-without light, we have no shadows.

What we’re doing is very common in math-we take a real world situation, and put it in an “ideal world” so we can find out more about it. Later on, we can apply the new things we’ve learned to the real world.

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