I have a real problem with this question, which may perhaps be perceived as pedantry, but to me is rather a bugbear. (Actually, it wasn't exactly this question, but the idea is equivalent.)

Clearly, the intent of the questioner is to elicit a response involving one of the 'special triangles' - half of an equilateral triangle, some Pythagoras and the definition of sin(x) as opposite / hypotenuse:

It is not the

*intent*of the question I have a problem with, but the specific wording. The 'solution' shown above does not

**In fact, I do not believe it is possible to**

*explain why*.*explain why*this fact is true, it simply

**is true.**Beyond the arbitrary definition of degrees and the arbitrary symbols used to represent the numbers and functions involved, the relationship in question is a

*necessary, must-be*maths fact - a universal constant, if you will.

It is no more possible to

*explain why*this fact is true than it is to

*explain why*pi equals 3.14159...

It just does. Indeed this question is more philosophical than it is mathematical - why does dividing the circumference of a circle by it's diameter always necessarily yield this particular constant? And then perhaps, could a universe exist with pi equal to (say) 4?

As I said, I have no problem with the intent of the question, it's just that the questioner did not mean '

*explain why'*, but rather '

*demonstrate that'*.

Perhaps this is a pedantic point. As long as the intention of the questioner is communicated to the student, they will be able to 'answer' it. Nevertheless, my teeth will remain well-gritted when I see a question like this.

## No comments:

## Post a Comment