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    Re: Compass Error Corection
    From: Joe Schultz
    Date: 2010 Jul 4, 09:14 -0700

    Apacherunner: you wrote "I use a sine, but then draw a little diagram illustrating the small angle approximation, so that the people in the class can see the origin of the rule."

    Yep, but I've learned to not start there, especially with Americans and our terrible math skills. Two minutes in the beginning saves a lot of "yes but" later.

    I start with two unit circles. One shows a chord and it's associated angle, with the chord drawn horizontally in the upper part of the circle. The other circle shows an angle with it's associated sine and complementary sine, with the cosine drawn "up" from the circle's center. They then, after I explain that sines are "new math" in a historical context, see that the sine is associated with a half chord, and they'll never confuse sine and cosine ==> "I won't be with you when you're traveling. Think back to our unit circle and the chord and the half chord."

    In the context of our 1 in 60 rule, the unit circle also shows how the sine changes with the angle.

    It's also a way to explain the universal sine law, when that time comes, by making the chord length equal to the circle's radius. People remember better if we choose to keep it simple and consistent.

    Joe

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