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How important is knowledge of trig identities for use in Calculus

The specific identity $$\tag{A} \tfrac{1}{1 - \sin{x}} + \tfrac{1}{1 + \sin{x}} = 2\sec^{2}{x}$$ as such is probably not often encountered, but simplifications akin to \...
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Why we don't normally teach chord, versine, coversine, haversine, exsecant, excosecant any more?

More of a comment than an answer but: They are all composites of more basic functions. In fact, all of the trig functions could can expressed in terms of sine, linear changes in coordinates, and ...
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Real-life problems involving solving triangles

There are many real-life problems involving solving triangles in "Trigonometry for the Practical Man" by James Edgar Thompson. Here are some from Chapter 5: Problem 1 From the top of a ...
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Memorizing Trig Identities

I agree this memorization is not necessary. If students understand how the trigonometric functions are defined (unit circle) and know several basic identities, everything else can be derived. I think ...
• 286
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Why is it written $\tan^{-1}$?

It's the functional inverse rather than the multiplicative inverse. Somewhere along the way, notation arrived at function composition being written as $f(f(x))=f^2(x)$, so the functional inverse ...
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Is $180^\circ = \pi$?

It is possible to treat degrees and radians as units, just as we treat inches and centimeters as units. Just as we can convert inches to centimeters (1 in = 2.54 cm), we can convert degrees to ...
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How important is knowledge of trig identities for use in Calculus

Due to low enrollment, my AP Calc class was filled with the students who otherwise would have taken Pre-Calc this year. So you can imagine that "How much do you really need to know to see the bigger ...
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Why teach reference angles?

I disagree with your statement on the usefulness of reference angles, they have more use in the plane of the unit circle. So to answer the question specifically, yes we should still teach them and one ...
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Why we don't normally teach chord, versine, coversine, haversine, exsecant, excosecant any more?

As several respondents have indicated, one could choose many different trigonometric functions to serve as the basic elements in terms of which other trigonometric functions are expressed and in (...
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Interesting Trigonometry problems

When introducing the sum of angle equations, I practiced presenting this. Starting with introducing a right triangle inside a rectangle. (I misplaced my notes, in which I had every step clearly laid ...

If you really want to understand why the curriculum is structured the way it is, and how it got that way, you might want to read a brief history of the discourse around geometry education for the past ...
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Solving a Polar set of equations algebraically?

This might not quite be an "algebraic" solution in the sense the student was looking for, but I think a more reasonable approach to this sort of problem is using bounds, not setting things equal from ...
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Memorizing Trig Identities

If you have lots of time then you can surely derive most of the identities from the basics but basically it slows down your learning when these identites are required. Also not memorising these will ...
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I cannot speak to curricula outside of the US, and I don't really buy your argument that geometry courses are "focused more on memorizing theorems rather than understanding where they come from." It ...
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How to intuitively understand how the trig ratios are calculated

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 ...
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How to layout a solution to a trig equation?

In most mathematics classes, we don't actually care about the solution to an exercise. The point is to get students to practice with the concepts, and figure out how to communicate their thinking. ...
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