## lilsis76 3 years ago graph each point in a polar coordinate system then convert the given polar coordinates to rectangluar coordinates. can someone help me do this step by step so i understand please. 1) a) (3, 2pi/3)

1. ByteMe

|dw:1351734596209:dw| notice that the point will have a negative x, positive y coordinates...

2. lilsis76

why would it be negative?

3. ByteMe

use... $$\large x=rcos\theta$$ $$\large y=rsin\theta$$

4. ByteMe

because the point is in the second quadrant....

5. ByteMe

|dw:1351734804583:dw|

6. lilsis76

7. lilsis76

|dw:1351734929718:dw|2pi/3....i dont see how that can be at that angle.

8. ByteMe

yes... r=3; $$\theta=\frac{2\pi}{3}$$

9. lilsis76

okay i see that .....

10. ByteMe

|dw:1351735004666:dw|

11. lilsis76

but shouldnt the 2pi/3 go on the bottom like in the 270 degree? ugh...or do i use calcutore to solve?

12. lilsis76

oh lol sorry, i got them mixed up

13. lilsis76

and why is it to the left of the graph? arent they positive?

14. ByteMe

|dw:1351735188538:dw|

15. ByteMe

16. lilsis76

okay, u see how u found the point in the left of the graph chart, why is it to the left. isnt it ( - , +) we have a (+,+)

17. lilsis76

do u get what i mean? cuz i see a positive point

18. ByteMe

oh... you're referring to the point $$\large (3, \frac{2\pi}{3})$$..... that point is represented in POLAR form, $$\large (r, \theta)$$ and not cartesian form (x, y)

19. lilsis76

|dw:1351735526253:dw|

20. lilsis76

okay but why doesnt the 3 go to the right?

21. ByteMe

22. ByteMe

here... click on this link... http://www.mathwords.com/p/polar_rectangular_conversion_formulas.htm

23. lilsis76

okay then, so looking at the unit circle its the point then, and like u said the 3 is the radius. so thats the reason why its to the left. It says now to convert the given polar coordinates to rectangular coordinates

24. lilsis76

how would i start this one?

25. ByteMe

no... the reason why it's on the left of the y-axis is because the angle theta, 2pi/3 resides in the second quadrant.

26. ByteMe

here... this is a better explanation of polar coordinates: http://www.mathsisfun.com/polar-cartesian-coordinates.html

27. lilsis76

okay ill look at it

28. ByteMe

so those formulas i gave you converts the given point in POLAR form to RECTANGULAR form...

29. lilsis76

okay. let me try on here and u let me know if i do it wrong. please.

30. ByteMe

ok...

31. lilsis76

x= r cos theta --> 3 cos 2pi/6 --> 3(1/2) --> 3/2 y= r sin theta --> 3 sin 2pi/6 --> 3(sqrt.3 /2) --> 3/2 sqrt3

32. ByteMe

why is the angle 2pi/6 ??? i thought it was 2pi/3 ???

33. lilsis76

AH! sorry, haha i was looking at a 6. let me try

34. lilsis76

x= r cos theta --> 3 cos 2pi/3 --> 3(1/2) --> 3/2 y= r sin theta --> 3 sin 2pi/3 --> 3(sqrt.3 /2) --> 3/2 sqrt3

35. ByteMe

careful.... $$\large cos(\frac{2\pi}{3})=-\frac{1}{2}$$

36. ByteMe

37. lilsis76

oops, thanks, okay so then x= r cos theta --> 3 cos 2pi/6 --> 3(- 1/2) --> - 3/2 y= r sin theta --> 3 sin 2pi/6 --> 3(sqrt.3 /2) --> 3/2 sqrt3

38. ByteMe

yes... so the x y coordinate for the point is $$\large (-\frac{3}{2},\frac{3\sqrt3}{2})$$

39. lilsis76

|dw:1351736659036:dw| then the coordinate - 3/2, 3 sqrt 3 /2 would be in the same area right?

40. ByteMe

it is the SAME point.... only expressed in cartesian form

41. lilsis76

oh...okay, let me try the other problems and ill be back online if I need help. THANK YOU!!!

42. ByteMe

43. ByteMe

good luck... :)

44. lilsis76

thanks