# Phase shift or phase angle?

By Murray Bourne, 30 Dec 2006

In the section Graphs of y = a sin (bx + c) in the Interactive Mathematics site, I have a statement

NOTE:Phase angle is not the same as phase shift.The phase angle for the sine curve y = a sin(bx + c) is the value of c and the phase shift is given by -c/b [...].

Alan Cooper, of alQpr commented:

The use of the term "phase shift" to represent the horizontal shift of a graph is almost universal among high school teachers and text authors at that level, but is, I believe, contrary to the majority usage among university mathematics and physics communities as well as in applied fields. While the proposed distinction between "phase shift" and "phase angle" might be one way of saving face for the teachers, I do not think it is appropriate to require students to adopt linguistic conventions that are not essentially universal, and indeed it is better to let them know that some terms are used differently in different professional communities - and then to refrain from having their grades depend on whether they follow one or other of those conventions.

In my opinion, what high school math teachers do with the notion of phase is worse than having them not mention the topic at all.

He raises an important point here. Are we presenting mathematics for high school students so they can pass some exam (adopting specific linguistic conventions decided on by the assessment writers) or is it what it should be - an insight into how mathematics is used in the "real world"?

Actually, when developing mathematics materials, I have struggled with the desire to keep it simple for newbies, but also to keep it useful so that when students see it again in their physics, chemistry, biology or engineering classes, they will recognise it and will know what to do with it.

Throughout my site, I have tried to use simple variables (I tend to use a, b, c rather than Greek ξ ς χ ψ) in the desire to keep the notation as easy to read as possible. But in a way, this does a disservice to students since they freak out when their other subjects use much more difficult notation. We expect students to be able to transfer their knowledge, but many find it impossible. We leave out too many of the interesting complexities in the desire to make sure they all get it.

So back to the issue of phase shift and phase angle. If I remove the statement defining the difference, my engineering students will miss an important distinction. Thoughts from anyone else on this?

**Footnote1 :** One of the most confusing things that engineering lecturers do, I feel, is to mix radians and degrees in the same expression. The vast majority of students struggle with radians and I try to keep them separate from degrees where possible.

**Footnote 2:** When someone challenges you like this, it is good for learning. When you have to justify what you have done, it motivates you to do more reading and thinking. In schools, we don't do enough of Arguing to Learn.

See the 16 Comments below.