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You have to observe that $$Opposite = \frac{Opposite}{Adjacent}*Adjacent = \frac{Opposite}{Hypothenuse}*\frac{Hypothenuse}{Adjacent}*Adjacent = \frac{\sin(\theta)}{\cos(\theta)} *Adjacent= \tan(\theta)*Adjacent$$. So you start with an unsual math-trick and multiply by one. Now you can concentrate on $\frac{Opposite}{Adjacent} =\frac{\sin(\theta)}{\cos(\... 0 Like the other answers, I'd also suggest lots of computations for many triangles of increasing steepness. This way students could gradually figure out what the curves are like, what the domains and ranges are, and where it increases, decreases, etc. They could sketch approximations of the functions? So, for example with$\tan(62)$, even if they don't know ... 2 The common way to introduce how trig functions are calculated numerically is via Taylor/Maclaurin series. These are used extensively in a lot of engineering and physics based applications. However, this requires a knowledge of calculus, and isn't very useful in the context of basic trigonometry. It also isn't useful for giving students a "feel" of how these ... 6 May I suggest giving them a bit of header code? i.e. Instead of using from math import sin try import math def sin(theta): return math.sin(math.radians(theta)) 0 There are a lot of approaches to approximating sine and cosine which would be sensible to a high school audience. One method is to use the double angle formula repeatedly, together with small angle approximations. For instance, if you want to approximate$\sin(\theta)$and$\cos(\theta)$, approximate$\sin(\theta/64) \approx \theta/64$and$\cos(\theta/64)...

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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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Although, I do not have any recommendation for trigonometry text and most of the arguments for & against seems valid here. But I do want to point out, SL Loney is widely used as a reference textbook in India for Trignometry & Coordinate geometry. Any student who is serious about qualifying the university entrance exams must solve part 1 of the Loney'...

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