## AonZ 2 years ago Eliminate A from each pair of parametric equations x = 3sinA y= 6sin2A

1. dan815

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2. dan815

is it like that or is it sin^2A

3. AonZ

its sin2A 2sinAcosA

4. dan815

ok

5. jdoe0001

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

6. AonZ

x/3?

7. jdoe0001

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

8. AonZ

the question is x = 3sinA

9. jdoe0001

ok

10. genius12

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

write the equation simply without A

12. jdoe0001

@genius12 pretty much, is just conversion to rectangular

13. genius12

So y in terms of x and not A right?

14. AonZ

yes

15. genius12

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

16. dan815

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17. dan815

18. jdoe0001

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19. dan815

lol

20. dan815

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

21. genius12

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

^ true

23. jdoe0001

right :)

24. AonZ

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

25. dan815

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26. dan815

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27. genius12

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

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

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

30. dan815

u dont need to they just want an equation without A

31. jdoe0001

right, so I notice

32. AonZ

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

33. dan815
34. AonZ

was hard to read dan's writting :P

35. dan815

if u wanna see a nice graph :)

36. AonZ

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

37. AonZ

last question :)

38. jdoe0001

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

39. 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

40. dan815

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41. dan815

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

42. dan815

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

43. dan815

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44. dan815

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45. dan815

see if that helps

46. dan815

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

47. dan815

brb

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