## music101 one year ago Convert the polar equation to rectangular form and identify the graph. r= 7/ (2cosΘ+5sinΘ)

1. music101

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2. sourwing

y = r sin(theta) x = r cos(theta) x^2 + y^2 = r^2 plug and chug

3. music101

yea so how would i plug it in

4. music101

cuz i did this last week and i kinda forgot sorry

5. myininaya

Try getting your cos and sin with r over there by multiplying both sides by 2cos(theta)+5sin(theta)

6. music101

okay. i did that

7. myininaya

So you have: $2rcos(\theta)+5rsin(\theta)=7 ?$

8. music101

why would you put r w/ each one of the terms isnt there just 1?

9. myininaya

$r=\frac{7}{2\cos(\theta)+5 \sin(\theta)} => r(2\cos(\theta)+5 \sin(\theta))=7$ Distributive property!

10. music101

oh ok i gotchu

11. myininaya

you should have it from here. Use the equations sour gave you.

12. music101

thannk you(:

13. music101

what if the question's like r= -3sinΘ ?

14. myininaya

Try multiplying r on both sides recall rsin(theta)=y and r^2=x^2+y^2

15. music101

hmm ok...

16. music101

so r^2= -3rsinΘ?

17. myininaya

right so now you are able to replace rsin(theta) with y and r^2 with x^2+y^2

18. music101

okay

19. music101

then youd have?

20. music101

the square root of that right?

21. myininaya

just do exactly what I said replace r sin(theta) with y replace r^2 with x^2+y^2

22. music101

i did tht

23. myininaya

you are done what else do you want?

24. music101

25. music101

oh ok

26. myininaya

putting an equation in terms of just x and y ( or just x or just y) is called a cartesian equation if that was the directions to just right as a cartesian equation then you are done

27. myininaya

write*

28. music101

right, sorry. i missed a problem on my homework it was r= 2sinΘ-4cosΘ

29. myininaya

multiply both sides by r

30. music101

do you square both sides 1st

31. music101

thts what i emant

32. myininaya

replace r^2 with x^2+y^2 replace r sin(theta) with y replace r cos(theta) with x

33. music101

ok i did that: x^2+y^2= 2y-4x

34. myininaya

yep. :) that is right you wrote the poloar equation as a cartesian equation if that is all the directions said to do then you are done.

35. music101

do you stop there

36. music101

ok

37. music101

aand i missed r= 3+3cosΘ

38. music101

so i multiplied both sides by r 1st

39. music101

and got x^2+y^2=3r +3x but dont i need to get rid of the r?

40. myininaya

you could subtract both sides by 3x giving you $x^2+y^2-3x=3r$ then square both sides and replace the r^2 with x^2+y^2

41. music101

why square both sides?

42. myininaya

43. music101

so what would be final answer then

44. myininaya

what if you with what I was saying take my equation and then square both sides and then replace the r^2 with x^2+y^2 you will have your final answer

45. music101

yeah but when you square the whole left side you get x^4+y^4-9x^2 = 3x^2+y^2?

46. myininaya

$(x^2+y^2-3x)^2=(3r)^2$ the us what you get when you square both sides your equation is not equivalent to that you squared each term sorta but not really it is whatever you do to one side of equation you can do to the other and the equation still holds

47. myininaya

$\text {recall law of exponents} (3r)^2=3^2r^2=9r^2=9(x^2+y^2)$

48. music101

so..

49. music101

im not following are you saying keep left side just squared in parentheses?

50. myininaya

It is easier than multiplying it out, don't you think?

51. music101

yes. so only change right side. like substitue

52. myininaya

You can multiply it out if you want. Just do it correctly, but the if the directions just say write as a rectangular (aka cartesian equation) than you are done. If the left hand side was already in terms of x and y. r^2 was the only thing that needed to be converted.

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