AonZ
Eliminate A from each pair of parametric equations
x = 3sinA
y= 6sin2A
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dan815
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|dw:1369436912384:dw|
dan815
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is it like that or is it sin^2A
AonZ
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its sin2A
2sinAcosA
dan815
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ok
jdoe0001
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from x= 3sin(a), what would sin(a) be?
AonZ
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x/3?
jdoe0001
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.. right... ... is x= 3sin(a), what you have or x = 3cos(a)?
AonZ
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the question is x = 3sinA
jdoe0001
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ok
genius12
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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
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write the equation simply without A
jdoe0001
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@genius12 pretty much, is just conversion to rectangular
genius12
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So y in terms of x and not A right?
AonZ
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yes
genius12
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\[\bf x=3\sin(A) \implies \frac{x}{3}=\sin(A) \implies \sin^{-1} \left( \frac{x}{3}\right)=A\]Plug this value of A in y = 6sin(2A) and you're done.
@AonZ
dan815
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|dw:1369437576413:dw|
dan815
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is that readable
jdoe0001
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dan815
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lol
dan815
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well he shudnt get the asnwer too easily so its all good :)
genius12
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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
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^ true
jdoe0001
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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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genius12
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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
genius12
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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
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not sure you can get rid of the "x" though, I got the same :S
dan815
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u dont need to they just want an equation without A
jdoe0001
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right, so I notice
AonZ
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thank you so much :D
understood @genius12 way much better
AonZ
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was hard to read dan's writting :P
dan815
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if u wanna see a nice graph :)
AonZ
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last question :)
jdoe0001
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just post in the channel, so we can all see it and thus help :)
dan815
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dan815
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2 ways to go from cosa to a/2 or other way, which trig u know
dan815
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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
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see if that helps
dan815
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look at the formula for Cos(2a) and that tan^2a either one of those will help you simplify and eliminate a
dan815
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brb