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# Parametrics watch

1. grr i was doing maths revision and decided to pick the MOST EVIL QUESTION in the whole wide world!

x = ?sin? + cos?
y = ?cos? - sin?

find the equation of the curve...

i do know that sin²? + cos²? = 1 plays a part, but im confused as what to do
can anyone help? (i need a dummy's guide to answering this question )
any help is greatly appreciated
2. grr
the qn mark = theta
3. (Original post by hel437)
grr i was doing maths revision and decided to pick the MOST EVIL QUESTION in the whole wide world!

x = ?sin? + cos?
y = ?cos? - sin?

find the equation of the curve...

i do know that sin²? + cos²? = 1 plays a part, but im confused as what to do
can anyone help? (i need a dummy's guide to answering this question )
any help is greatly appreciated
I am sure I remember doing this one ages ago...

x + y = 2cosθ
x - y = 2sinθ

=> (x + y)² + (x - y)² = 2²cos²θ + 2²sin²θ = 2²

=> x² + 2xy + y² + x² - 2xy + y² = 4

=> 2x² + 2y² = 4

=> x² + y² = 2

Is that right?
4. i might just be having a stupid day...but i dont get how you get x+ y = 2cos theta..or the x - y = 2sin theta
5. (Original post by hel437)
i might just be having a stupid day...but i dont get how you get x+ y = 2cos theta..or the x - y = 2sin theta
x = sinθ + cosθ
y = cosθ - sinθ

so: x + y = sinθ + cosθ + cosθ - sinθ = 2cosθ

and: x - y = sinθ + cosθ - cosθ + sinθ = 2sinθ
6. but its theta sin theta in x and theta cos theta in y...argh! so confused..
im really appreciating your help
7. (Original post by hel437)
but its theta sin theta in x and theta cos theta in y...argh! so confused..
im really appreciating your help
Oh is it! Sorry...

Are you sure?

Where is this from?
8. its ex 4b question 1 vi) in the P3 MEI text book. i dont think i copied it down wrong, bt i dont have access to the textbook at this very moment. it wasnt an exam question, so its not hugely important. but its starting to annoy me now.
9. Do you have an answer?
10. x = φsinφ + cosφ
y = φcosφ - sinφ

x² = φ²sin²φ + 2φsinφcosφ + cos²φ
y² = φ²cos²φ - 2φcosφsinφ + sin²φ

x² + y² = φ²(sin²φ + cos²φ) + (cos²φ + sin²)
x² + y² = φ² + 1
r² = φ² + 1
r = √(φ² + 1)
==========

Which is the polar eqn of a spiral.
11. i *just* realised i read the stupid question wrong. all i had to do was find dy/dx *bangs head on wall*
apologies to all those of you who tried (and succeeded in some cases) to work it out!
i really am having a stupid day
12. this question just asks for the differential so its just
dy/dx = dy/d0 x d0/dx

d0/dx= 1/dx/d0

dy/dx= (-θsinθ+cosθ- cosθ )/(θcosθ+sinθ- sinθ )
dy/dx= -θsinθ/θcosθ
dy/dx= -tanθ

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