I had a few minutes spare this morning and was inspired by a fellow tutors request for a Cos-rule song. So I had a play around and this is what I came up with. A little rhyme to try and help students recall the cos rule involving sides of a non-right-angled triangle.

If you want to read more about the cos rule you can have a look here.

Here is the ditty, please feel free to share:

The cos rule requires a little invention

the Pythagoras rule with a little extension

take away the 2bc, cos A’s not right

across from big A little a takes flight

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I’ve tried to include subtle reminders. The ending of line 3 cos A’s not right referred to the fact you don’t need the angle to be a right angle to use this rule. The last line is to remind the student that the angle you use should be opposite to the length you are trying to find.

Of course, I’m assuming that you usually remember the Pythagoras rule as . If you generally use the letters in a different combination the rhyme still works- you will just need to swap the letters. For example, if you use the rhyme would go:

The cos rule requires a little invention

the Pythagoras rule with a little extension

take away the 2ab, cos C’s not right

across from big C little c takes flight

What do you think? Do you have any other suggestions or rhymes that you use to help remember important information?

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This is great Alex, it’s got a catchy ring to it. It will certainly be useful as a memory aid when students are first learning the cosine rule. Once they have done enough questions on the cosine rule, they will remember it anyway…one would hope!

Thanks! Exactly – most students I have worked with get a grip of this equation fairly quickly. What I was going for here was to help with the connection that the rule can be used in triangles even when there isn’t a right angle. Also, to serve as a reminder that the angle in question should be opposite to the length we are trying to find. I guess a good starting point- with little reminders about the rule.