# Trigonometry

## What Are Trig Functions, Really?

(An archive question of the week) Trigonometric functions are sometimes introduced without a deep explanation of their meaning; they are just buttons to push on a calculator, or names to write in an equation. Even when a textbook gives a careful presentation, there are so many facets to the concept that it can be easy …

## Different Ways to Prove a Trigonometric Identity

Proving trigonometric identities can be a major challenge for students, as it is often very different from anything they have previously done. Often they confuse this concept with solving an equation. But also, they may be give overly rigorous standards to comply with. Here, I will look at several discussions we have had about different …

## Ranges of Inverse Trig Functions

(Archive Question of the Week) We have had a number of questions over the years about inverse trig functions and their ranges. For today’s question, I have chosen one from 2011, which will link to a number of others that I will not quote in detail.

## Averaging Angles

(Archive Question of the Week) An interesting question that has been referred to many times since it was written in 1999 deals with averaging angles. At first the question seems trivial; then almost impossible; and then we end up with a rather simple formula that is totally unlike what we started with. And further applications …

## Minimizing an Angle

(New Question of the Week) An interesting trigonometry problem came through about a month ago, answered by Doctor Rick. It gives a nice example of how our process works at its best. It is also an interesting problem!