AonZ
  • AonZ
Eliminate A from each pair of parametric equations x = 3sinA y= 6sin2A
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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dan815
  • dan815
|dw:1369436912384:dw|
dan815
  • dan815
is it like that or is it sin^2A
AonZ
  • AonZ
its sin2A 2sinAcosA

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More answers

dan815
  • dan815
ok
jdoe0001
  • jdoe0001
from x= 3sin(a), what would sin(a) be?
AonZ
  • AonZ
x/3?
jdoe0001
  • jdoe0001
.. right... ... is x= 3sin(a), what you have or x = 3cos(a)?
AonZ
  • AonZ
the question is x = 3sinA
jdoe0001
  • jdoe0001
ok
anonymous
  • 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
  • AonZ
write the equation simply without A
jdoe0001
  • jdoe0001
@genius12 pretty much, is just conversion to rectangular
anonymous
  • anonymous
So y in terms of x and not A right?
AonZ
  • AonZ
yes
anonymous
  • 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
  • dan815
|dw:1369437576413:dw|
dan815
  • dan815
is that readable
jdoe0001
  • jdoe0001
|dw:1369437887196:dw|
dan815
  • dan815
lol
dan815
  • dan815
well he shudnt get the asnwer too easily so its all good :)
anonymous
  • 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
  • dan815
^ true
jdoe0001
  • jdoe0001
right :)
AonZ
  • AonZ
|dw:1369437893899:dw| i dont it get when u went into that part
dan815
  • dan815
|dw:1369437924563:dw|
dan815
  • dan815
|dw:1369437958849:dw|
anonymous
  • 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
  • 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
  • jdoe0001
not sure you can get rid of the "x" though, I got the same :S
dan815
  • dan815
u dont need to they just want an equation without A
jdoe0001
  • jdoe0001
right, so I notice
AonZ
  • AonZ
thank you so much :D understood @genius12 way much better
dan815
  • dan815
http://www.wolframalpha.com/input/?i=%28y%2F%284x%29%29%5E2%2B%28x%2F3%29%5E2%3D1
AonZ
  • AonZ
was hard to read dan's writting :P
dan815
  • dan815
if u wanna see a nice graph :)
AonZ
  • AonZ
AonZ
  • AonZ
last question :)
jdoe0001
  • jdoe0001
just post in the channel, so we can all see it and thus help :)
AonZ
  • 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
  • dan815
|dw:1369438736058:dw|
dan815
  • dan815
2 ways to go from cosa to a/2 or other way, which trig u know
dan815
  • dan815
theres also an identity u can use straight from tan to a double angle
dan815
  • dan815
|dw:1369439021400:dw|
dan815
  • dan815
|dw:1369439046456:dw|
dan815
  • dan815
see if that helps
dan815
  • dan815
look at the formula for Cos(2a) and that tan^2a either one of those will help you simplify and eliminate a
dan815
  • dan815
brb

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