## AonZ Group Title Eliminate A from each pair of parametric equations x = 3sinA y= 6sin2A one year ago one year ago

1. dan815 Group Title

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2. dan815 Group Title

is it like that or is it sin^2A

3. AonZ Group Title

its sin2A 2sinAcosA

4. dan815 Group Title

ok

5. jdoe0001 Group Title

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

6. AonZ Group Title

x/3?

7. jdoe0001 Group Title

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

8. AonZ Group Title

the question is x = 3sinA

9. jdoe0001 Group Title

ok

10. genius12 Group Title

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. AonZ Group Title

write the equation simply without A

12. jdoe0001 Group Title

@genius12 pretty much, is just conversion to rectangular

13. genius12 Group Title

So y in terms of x and not A right?

14. AonZ Group Title

yes

15. genius12 Group Title

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

16. dan815 Group Title

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17. dan815 Group Title

18. jdoe0001 Group Title

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19. dan815 Group Title

lol

20. dan815 Group Title

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

21. genius12 Group Title

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.

22. dan815 Group Title

^ true

23. jdoe0001 Group Title

right :)

24. AonZ Group Title

|dw:1369437893899:dw| i dont it get when u went into that part

25. dan815 Group Title

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26. dan815 Group Title

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27. genius12 Group Title

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

28. genius12 Group Title

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.

29. jdoe0001 Group Title

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

30. dan815 Group Title

u dont need to they just want an equation without A

31. jdoe0001 Group Title

right, so I notice

32. AonZ Group Title

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

33. dan815 Group Title
34. AonZ Group Title

was hard to read dan's writting :P

35. dan815 Group Title

if u wanna see a nice graph :)

36. AonZ Group Title

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

37. AonZ Group Title

last question :)

38. jdoe0001 Group Title

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

39. AonZ Group Title

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

40. dan815 Group Title

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41. dan815 Group Title

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

42. dan815 Group Title

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

43. dan815 Group Title

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44. dan815 Group Title

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45. dan815 Group Title

see if that helps

46. dan815 Group Title

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

47. dan815 Group Title

brb