## lilsis76 Group Title 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) one year ago one year ago

1. ByteMe Group Title

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

2. lilsis76 Group Title

why would it be negative?

3. ByteMe Group Title

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

4. ByteMe Group Title

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

5. ByteMe Group Title

|dw:1351734804583:dw|

6. lilsis76 Group Title

7. lilsis76 Group Title

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

8. ByteMe Group Title

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

9. lilsis76 Group Title

okay i see that .....

10. ByteMe Group Title

|dw:1351735004666:dw|

11. lilsis76 Group Title

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

12. lilsis76 Group Title

oh lol sorry, i got them mixed up

13. lilsis76 Group Title

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

14. ByteMe Group Title

|dw:1351735188538:dw|

15. ByteMe Group Title

16. lilsis76 Group Title

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 Group Title

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

18. ByteMe Group Title

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 Group Title

|dw:1351735526253:dw|

20. lilsis76 Group Title

okay but why doesnt the 3 go to the right?

21. ByteMe Group Title

22. ByteMe Group Title

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

23. lilsis76 Group Title

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 Group Title

how would i start this one?

25. ByteMe Group Title

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 Group Title

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

27. lilsis76 Group Title

okay ill look at it

28. ByteMe Group Title

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

29. lilsis76 Group Title

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

30. ByteMe Group Title

ok...

31. lilsis76 Group Title

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 Group Title

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

33. lilsis76 Group Title

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

34. lilsis76 Group Title

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 Group Title

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

36. ByteMe Group Title

37. lilsis76 Group Title

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 Group Title

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

39. lilsis76 Group Title

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

40. ByteMe Group Title

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

41. lilsis76 Group Title

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

42. ByteMe Group Title