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

1. music101 Group Title

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2. sourwing Group Title

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

3. music101 Group Title

yea so how would i plug it in

4. music101 Group Title

cuz i did this last week and i kinda forgot sorry

5. myininaya Group Title

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

6. music101 Group Title

okay. i did that

7. myininaya Group Title

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

8. music101 Group Title

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

9. myininaya Group Title

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

10. music101 Group Title

oh ok i gotchu

11. myininaya Group Title

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

12. music101 Group Title

thannk you(:

13. music101 Group Title

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

14. myininaya Group Title

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

15. music101 Group Title

hmm ok...

16. music101 Group Title

so r^2= -3rsinΘ?

17. myininaya Group Title

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

18. music101 Group Title

okay

19. music101 Group Title

then youd have?

20. music101 Group Title

the square root of that right?

21. myininaya Group Title

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

22. music101 Group Title

i did tht

23. myininaya Group Title

you are done what else do you want?

24. music101 Group Title

25. music101 Group Title

oh ok

26. myininaya Group Title

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 Group Title

write*

28. music101 Group Title

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

29. myininaya Group Title

multiply both sides by r

30. music101 Group Title

do you square both sides 1st

31. music101 Group Title

thts what i emant

32. myininaya Group Title

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

33. music101 Group Title

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

34. myininaya Group Title

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 Group Title

do you stop there

36. music101 Group Title

ok

37. music101 Group Title

aand i missed r= 3+3cosΘ

38. music101 Group Title

so i multiplied both sides by r 1st

39. music101 Group Title

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

40. myininaya Group Title

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 Group Title

why square both sides?

42. myininaya Group Title

43. music101 Group Title

so what would be final answer then

44. myininaya Group Title

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 Group Title

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

46. myininaya Group Title

$(x^2+y^2-3x)^2=(3r)^2$ 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 Group Title

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

48. music101 Group Title

so..

49. music101 Group Title

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

50. myininaya Group Title

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

51. music101 Group Title

yes. so only change right side. like substitue

52. myininaya Group Title

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.