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

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dan815Best ResponseYou've already chosen the best response.0
is it like that or is it sin^2A
 11 months ago

jdoe0001Best ResponseYou've already chosen the best response.0
from x= 3sin(a), what would sin(a) be?
 11 months ago

jdoe0001Best ResponseYou've already chosen the best response.0
.. right... ... is x= 3sin(a), what you have or x = 3cos(a)?
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
the question is x = 3sinA
 11 months ago

genius12Best ResponseYou've already chosen the best response.1
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
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
write the equation simply without A
 11 months ago

jdoe0001Best ResponseYou've already chosen the best response.0
@genius12 pretty much, is just conversion to rectangular
 11 months ago

genius12Best ResponseYou've already chosen the best response.1
So y in terms of x and not A right?
 11 months ago

genius12Best ResponseYou've already chosen the best response.1
\[\bf x=3\sin(A) \implies \frac{x}{3}=\sin(A) \implies \sin^{1} \left( \frac{x}{3}\right)=A\]Plug this value of A in y = 6sin(2A) and you're done. @AonZ
 11 months ago

jdoe0001Best ResponseYou've already chosen the best response.0
dw:1369437887196:dw
 11 months ago

dan815Best ResponseYou've already chosen the best response.0
well he shudnt get the asnwer too easily so its all good :)
 11 months ago

genius12Best ResponseYou've already chosen the best response.1
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.
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
dw:1369437893899:dw i dont it get when u went into that part
 11 months ago

genius12Best ResponseYou've already chosen the best response.1
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
 11 months ago

genius12Best ResponseYou've already chosen the best response.1
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.
 11 months ago

jdoe0001Best ResponseYou've already chosen the best response.0
not sure you can get rid of the "x" though, I got the same :S
 11 months ago

dan815Best ResponseYou've already chosen the best response.0
u dont need to they just want an equation without A
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
thank you so much :D understood @genius12 way much better
 11 months ago

dan815Best ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=%28y%2F%284x%29%29%5E2%2B%28x%2F3%29%5E2%3D1
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
was hard to read dan's writting :P
 11 months ago

dan815Best ResponseYou've already chosen the best response.0
if u wanna see a nice graph :)
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
can i pls get help on 1 more question? http://openstudy.com/study#/updates/519ff981e4b04449b221f091
 11 months ago

jdoe0001Best ResponseYou've already chosen the best response.0
just post in the channel, so we can all see it and thus help :)
 11 months ago

AonZBest ResponseYou've already chosen the best response.0
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
 11 months ago

dan815Best ResponseYou've already chosen the best response.0
2 ways to go from cosa to a/2 or other way, which trig u know
 11 months ago

dan815Best ResponseYou've already chosen the best response.0
theres also an identity u can use straight from tan to a double angle
 11 months ago

dan815Best ResponseYou've already chosen the best response.0
look at the formula for Cos(2a) and that tan^2a either one of those will help you simplify and eliminate a
 11 months ago
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