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If you are teaching this at an introductory level, then the algorithm that calculators use today is going to go far over their heads. (It might go over MY head!) The story of how we developed increasingly accurate trig tables over the course of history would be an interesting topic of inquiry for advanced algebra / pre-calculus / calculus, but at the ...


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The common way to introduce how trig functions are calculated numerically is via Taylor/Maclaurin series. These are used extensively in a lot of engineering and physics based applications. However, this requires a knowledge of calculus, and isn't very useful in the context of basic trigonometry. It also isn't useful for giving students a "feel" of how these ...


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You could look at separable differential equations: Given a differential equation of the form $$g(y)y'(x) = f(x),$$ integrating between $x_0$ and x on both side and integration by substitution with $u = y(x)$ gives $$\int_{x_0}^xg(y)y'(x) dx = \int_{x_0}^xf(x)dx $$ $$\int_{y(x_0)}^{y(x)}g(u) du = \int_{x_0}^xf(x)dx,$$ which allows to solve the ...


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