# Sin, cos, tan - daft question

Discussion in 'Mathematics' started by florapost, Jun 16, 2011.

1. ### florapost

i teach junior school and have forgotten so much ks 3/4 stuff it's ks3/4. so - i want to do a quick romp thro sin and cos with y6 ('cos we're going to have a look at euler's identity)
now - i start of with a ra triangle and show what sin and cos are. then i show the graphs
how do i justify the graphs going beyond 0 to pi/2 ?
in small, easy words?

2. ### bombaysapphireStar commenter

Find an animation of the triangle being formed within a unit circle.
If you have Autograph then there is an Autograph extras page with an animation of this. I would guess that you could google it and find similar.

4. ### florapost

lovely - thanks
they're the sort who will ask!

6. ### brookes

I wonder if it's a good idea to do this Flora. If they are going to ask lots of questions as you predict they will, I feel you need to know your stuff inside out.

7. ### florapost

i've got the rest of it, honest - i can differentiate e^itheta no problem - just couldn't get my head round this bit

8. ### NazardNew commenter

But your Y6 class sound a bit bright. Can you do it from first principles?

9. ### florapost

do which bit?

10. ### KYPNew commenter

Complex numbers? Further maths A Level? Please come and teach my 6th form class! What are you planning to do with Euler's identity?

Why?

12. ### DMNew commenter

I wanted to say that but decided against it because I like flora and didn't want to offend her. You do serve many purposes RF.

13. ### ResourceFinder

I hope that I did not offend

14. ### brookes

I have also deleted a few replies because I don't wish to offend Flora.

15. ### florapost

just spent 5 minutes explaining what i was going to do and stupid forum bounced me out!!!!!
we did complex numbers last term- have also done binary, so that deals with the one and the zero
so: looking at + , x and exp as basic functions
then looking at branches of maths - see if anyone's heard of calculus - tangents to curves (we've looked at conics, so parabola good) - basic differentiation
introduce e as series - see if they can diff e^x - if enough find it easy, we'll try e^ix from first principles - otherwise will just tell them and have hand out for those who want to go thro it at home (4 at a guess)
sin and cos graphs and radians - will just give differentail of sin and cos (but need graph to show diff possible) - handout again for those who wish to pursue it
et voila - euler
because it's the most beautiful thing in maths (we've already had the carol vordermann joke, folks)
this year's y6 are scarily bright - the best group i've had for 7 years - won the school &pound;100 in a maths comp, and didn't do better cos they were 'too bright, so not explaining their thought processes explicitly enough' -we have already done euclid's postulates 'cos they asked do triangles always have 180deg - and they worked out why the answer is 'not necessarily*
i also have to do a lesson on 'what does the earth weigh' at their request - heaven knows how long, on and off, that has taken me to compile

16. ### DMNew commenter

I'm sure she will realise you were not having a pop.

17. ### DMNew commenter

If mathematics were a jar of peanut butter, flora would use it all up, screw the lid back on and pop it back in the cupboard.
Save some for the rest of us!

18. ### florapost

not a bit offended - the thing so, they are bright, but also creative and off-the-wall (we did infinities before half term - i was thinking of it anyway, but one of them came up to me and asked about hilbert's hotel anyway) - and i eas asked,what was the most amazing thing i knew in maths, so i thought we'd go for it
i work in a weird school - a third of the kids at least are sen - kids try to kill each other in the playground - but we have always had an amazing top cohort - partly cos they're stretched academically, also because we offer scads of music, sport, trips and creative work. kids who've been thro the school love what they know when they get to secondary school that make their teachers
this will be strictly a once-in-7-years topic though

Knife.
Down.
Now.

20. ### florapost

dm - i actually do very little ks3+ maths - quite on purpose - it's what i was asked to do when i started, but i don't see the point - we just romp through the weird and wonderful -and i don't expect them to remember too much detail, more basics, like what i is and time being the extra dimension - otherwise, we do logic, number puzzles, sideways-on stuff and maths history as a deliberate policy so they're not going to be sitting at secondary school
the old dep head use to caoch kids for gcse maths