**A picture paints a thousand words**

Most people and pupils* are pretty comfortable with using degrees to measure angles. Whilst 360^{o} might seem an arbitrary number to split a complete rotation into, it makes sense to most.

But in A-Level maths (and beyond) the humble degree doesn’t always cut it, and students are introduced to Radians, often shortened to ‘Rads’, as a means of measuring angles.

The definition of a radian goes something like this:

The

radianis the standard unit of angular measure, used in many areas of mathematics. An angle’s measurement in radians is numerically equal to the length of a corresponding arc of a unit circle, so one radian is just under 57.3 degrees (when the arc length is equal to the radius).

Which is all well and good, but is a bit dry and less than illuminating.

Which is why I was so delighted to stumble across the animation at the top of this post which quickly, visually and with the minmum of fuss explains what a radian is – in this case, a picture really is worth a thousand words.

The picture isn’t mine – it was created by LucasVB, you can read his blog post about radians here and you can see the gallery of the animations he has created for Wikipedia here. A talented bloke.

I wanted to post the pic in my blog for two reasons:

- (Rather selfishly) I wanted a copy of the animation that I would always be able to find
- Its such a great explanation of Radians that I figure it deserves the widest possible audience

So, if you find yourself teaching radians, or your son or daughter asks “What’s a rad” – show them the image above and all will become clear.

*Not a very good sentence as, of course, pupils are a subset of people.

## 2 Comments

I’m thinking of showing the animation first and then letting students write their own definition of a radian. Then compare and contrast with the textbook definition. Here’s another website the advertises 7 animations that will make you understand trigonometry. I found it very helpful as well. Thanks for your post.

http://www.businessinsider.com/7-gifs-trigonometry-sine-cosine-2013-5

Hi Jim – thanks for your comments.

I think that’s a great idea: showing the animation first and then asking students to come up with a definition for a radian – crucially, it’ll will get them to

thinkwhich will help them to understand and retain that understanding, even if they don’t come up with the exact definition of a radian in the first place.I’m a great believer in

notjust spoon feeding pupils – let them explore, investigate, make mistakes; its the best way to learn.Thanks for the link to the website with trigonometry animations – well worth a visit.

Let us know how you get on,

Thanks again,

A Maths Teacher