Eliminate A from each pair of parametric equations
x = 3sinA
y= 6sin2A

- AonZ

Eliminate A from each pair of parametric equations
x = 3sinA
y= 6sin2A

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- schrodinger

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- dan815

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- dan815

is it like that or is it sin^2A

- AonZ

its sin2A
2sinAcosA

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## More answers

- dan815

ok

- jdoe0001

from x= 3sin(a), what would sin(a) be?

- AonZ

x/3?

- jdoe0001

.. right... ... is x= 3sin(a), what you have or x = 3cos(a)?

- AonZ

the question is x = 3sinA

- jdoe0001

ok

- anonymous

Btw, what do you mean by eliminate? Are you to convert this in to a rectangular equation with y in terms of x or are you to have both x and y written in terms of something else that isn't A?
@AonZ

- AonZ

write the equation simply without A

- jdoe0001

@genius12 pretty much, is just conversion to rectangular

- anonymous

So y in terms of x and not A right?

- AonZ

yes

- anonymous

\[\bf x=3\sin(A) \implies \frac{x}{3}=\sin(A) \implies \sin^{-1} \left( \frac{x}{3}\right)=A\]Plug this value of A in y = 6sin(2A) and you're done.
@AonZ

- dan815

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- dan815

is that readable

- jdoe0001

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- dan815

lol

- dan815

well he shudnt get the asnwer too easily so its all good :)

- anonymous

Both @dan815 and mine rectangular forms work. Except his makes it more obvious that cosine and sine can be used parametrically to give an ellipse as dan's rectangular form is the equation of an ellipse.

- dan815

^ true

- jdoe0001

right :)

- AonZ

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i dont it get when u went into that part

- dan815

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- dan815

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- anonymous

Rearrange x and y so that:\[\bf \frac{y}{4x}=\cos(A) \ and \ \frac{x}{3}=\sin(A)\]Squaring both sides of both equations gives:\[\bf \left( \frac{y}{4x} \right)^2=\cos^2(A) \ and \ \left( \frac{x}{3} \right)^2=\sin^2(A)\]Adding both equations and using the identity cos^2(A) + sin^2(A) = 1 gives u the rectangular form.
@AonZ

- anonymous

I just realised, @dan815 rectangular form actually won't be an ellipse even thought i looks like it will be lol. There is an x in the denominator under y which means it can't be the equation of an ellipse.

- jdoe0001

not sure you can get rid of the "x" though, I got the same :S

- dan815

u dont need to they just want an equation without A

- jdoe0001

right, so I notice

- AonZ

thank you so much :D
understood @genius12 way much better

- dan815

http://www.wolframalpha.com/input/?i=%28y%2F%284x%29%29%5E2%2B%28x%2F3%29%5E2%3D1

- AonZ

was hard to read dan's writting :P

- dan815

if u wanna see a nice graph :)

- AonZ

can i pls get help on 1 more question?
http://openstudy.com/study#/updates/519ff981e4b04449b221f091

- AonZ

last question :)

- jdoe0001

just post in the channel, so we can all see it and thus help :)

- AonZ

got a link :P http://openstudy.com/study#/updates/519ff981e4b04449b221f091
but Question is
Eliminate A from each pair of parametric equations
x = 2tan( A/2)
y = cosA

- dan815

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- dan815

2 ways to go from cosa to a/2 or other way, which trig u know

- dan815

theres also an identity u can use straight from tan to a double angle

- dan815

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- dan815

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- dan815

see if that helps

- dan815

look at the formula for Cos(2a) and that tan^2a either one of those will help you simplify and eliminate a

- dan815

brb

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