# Month: September 2023

## … And The Oldest Has Red Hair

It’s been a while since we’ve done a puzzle, just for fun. Here we’ll look at two versions of a riddle, about finding children’s ages from a known product, a partially known sum, and a bizarre fact about the oldest. Then we’ll close with an interesting variation.

## Monotonic Functions, Inequalities, and Optimization

Looking for a cluster of questions on similar topics, I found several from this year in which monotonic functions (functions that either always increase, or always decrease) provide shortcuts for various types of problems (optimization with or without calculus, and also algebraic inequalities). We’ll look at a few of these.

## Trig Terminology: What Do Those Words Mean?

Students sometimes wonder why the trigonometric functions (sine, cosine, tangent, secant, and so on) have the names they do, and how they relate to the corresponding terms in geometry. How are the tangent and secant functions related to tangent and secant lines in trigonometry? And what in the world is a sine? Here we’ll look …

## Inverse Trig Notation: What Do sin^-1 and arcsin Mean?

Since we’ve been looking at an example of ambiguity in notation, let’s look at a very different one. There is a lot to be confused by in inverse trigonometry! We’ll try to untangle the notations of $$\sin^{-1}$$ and $$\arcsin$$.

## Implied Multiplication 3: You Can’t Prove It

This is the last of a series on our discussions, since I closed comments at the end of 2021, of Implied Multiplication First (IMF), the idea that multiplications written by juxtaposition, rather than with a symbol, are to be done before other multiplications or divisions. Last time, we saw that there is no “official” answer. …