# Tag Info

Accepted

### How important is knowledge of trig identities for use in Calculus

The specific identity \begin{equation}\tag{A} \tfrac{1}{1 - \sin{x}} + \tfrac{1}{1 + \sin{x}} = 2\sec^{2}{x} \end{equation} as such is probably not often encountered, but simplifications akin to \...
Accepted

### May we permit identities to be established by equivalent equations?

Well, if their "equivalences" are in fact equivalences, then everything is fine. The problem seems to be mostly a psychological one: When students want to verify an equivalence, they check the left-...
Accepted

### Is Plane Trigonometry by S. L. Loney still good as a textbook today?

I started my career as an archaeologist before I ended up in mathematics. I say this in order to emphasize that I am interested in trying to understand how people thought in the past—the usual "...

### Should word problems be reasonable?

Physically (or even economically) unreasonable answers are confusing. The student needs to be shown that math is a tool that can solve practical problems. Answers that are unreasonable send the ...

### Symmetry in polar functions - how to explain

The problem underlying the discussion in the question can be summarized as that it is necessary to choose a branch cut to define a complex logarithm (or arctangent). It is a mistake and pedagogically ...

### Is Trigonometry done differently in the US?

As you've tagged this as precalculus, I'll say that there is no standard precalculus curriculum in the United States and very little "official" guidance about what such a curriculum should ...
Accepted

### Rules to eliminate erroneous solutions in Trig equations?

This isn't specific to trigonometry at all; it's really about understanding what it means to "solve an equation". Given functions $f, g: \mathbb{R} \to \mathbb{R}$, to solve the equation $f(x) = g(x)$ ...

### 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 ...

### May we permit identities to be established by equivalent equations?

When you solve an algebraic equation like $2x - 4 = 0$, what you're really doing is finding assignments for the variables assuming the given equation is true. Doing the same thing to both sides of an ...