Dave Peterson

(Doctor Peterson) A former software engineer with degrees in math, I found my experience as a Math Doctor starting in 1998 so stimulating that in 2004 I took a new job teaching math at a community college in order to help the same sorts of people face to face. I have three adult children, and live near Rochester, N.Y. I am the author and instigator of anything on the site that is not attributed to someone else.

An Introduction to Trigonometry

(An archive question of the week) While I’m showing some recent explanations of basic trigonometry techniques, this is a good time to look at an even more basic explanation of the essentials of the subject for a beginner. Right triangle trigonometry Here is the question, from 2001: Trigonometry in a Nutshell I’m in 8th grade …

An Introduction to Trigonometry Read More »

Equations with Fractions: Three Ways to Solve Them

Since we just looked at a complicated rational inequality, let’s look at some simpler rational equations, first a linear equation with fractions, and then truly rational equations, in which the variable(s) appear in the denominator. This discussion dealt with a common confusion I’ve seen in students. The problem The question came from Fairooz in 2017: …

Equations with Fractions: Three Ways to Solve Them Read More »

A Rational Inequality with Huge Exponents

When a challenging type of problem is written with unexpectedly large numbers, it can look impossible. Today’s discussion illustrates how to get past the hurdles. The problem The problem came from Arsh in April: Q) [x((x+5)^2016)((x-3)^2017)((6-x) ^1231)]/((x-2)^10000)((x+1)^2015)((4-x)^242) ≥ 0 Since our site doesn’t yet allow LaTeX formatting, and Arsh chose not to insert the problem …

A Rational Inequality with Huge Exponents Read More »

How Many Different Pizzas?

(An archive question of the week) We’ve been looking at examples of extended discussions with students about various kinds of problems. Here, we have one (not from a student) that led to some good thinking about combinatorics – the techniques of counting the ways something can happen. The problem: Triple toppings Here’s the question, from …

How Many Different Pizzas? Read More »