Cartesian points in polar coordinates.

AI Thread Summary
To convert the Cartesian point (3, 3) into polar coordinates, the radial distance (r) is calculated using the formula r = √(x² + y²), which results in r = 3√2. The angle (θ) formed with the positive x-axis is 45 degrees, leading to the polar coordinates being expressed as (3√2, 45°). The discussion emphasizes the importance of understanding the relationship between Cartesian and polar coordinates, particularly through visualizing right triangles. Participants encourage using resources like textbooks and Wikipedia for better comprehension. The final consensus confirms that the polar coordinates for the point (3, 3) are indeed (3√2, 45°).
lakitu
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Hey everyone, my lecture has given me this question, I am unsure where to start with it.

Express the Cartesian point (3, 3) in polar coordinates.

Do i need to use the sin and cos on my calc.

Any help would be very helpful

lakitu
 
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Instead of resorting to a calculator, draw the line segment from the origin to the point (3,3).
What is the angle this line segment makes with the positive x-axis?
 
lakitu, you could have done some research. That's one good thing I learned from this forum. I didn't learn yet polar coordinates and I think I can resolve this exercise by simply reading wikipedia's introduction on polar coordinates.

See- http://en.wikipedia.org/wiki/Polar_coordinates
 
your right, i guess i assumed it was a little tougher than it was :)

to arildno: Is the angle 45 deg ? would that make the answer (3,45)

kind regards lakitu
 
Look again at the radial component. How far is it from the origin to (3,3)?
 
im not sure what you mean? i can only think the distance is 6 if its not 3 what i originally believed :)
 
i read that the position of the point is defined by its direct distance from the origin (O) do you measure this with a ruler? I am just unsure :)
 
lakitu, see the introduction of wikipedia and the formula to determine the radial distance from the pole and think if it really is 6 or 3 or 3\sqrt{2}.
 
Would you please show us the relationship between polar and cartesian coordinates.
 
  • #10
i found this example in my textbook, r = sqrt(x*x + y*y) a = atan(y / x) which would give me the distance of 4.24 for r (the origin to 3,3)

so would the answer be (4.24,45deg)?

i did read your recomendations but struggled to figure those out :)

am i on the right lines ?
 
  • #11
Yes. That's right. :approve:
But you could use instead of the approximated 4.24 the precise r, which is 3\sqrt{2}.
 
  • #12
wow at last! I think i am going to have to change my username after this topic!

thanks
 
  • #13
Could you explain to me how you work out that the precise r is 3\sqrt{2} ?

Thank you
 
  • #14
What is the length of the hypotenus of a right triangle when both of the other sides have length 1?
 
  • #15
lakitu, follow Integral's suggestion. I would have explained to you how do to it, but you would't learn as well as you will if you think for yourself.
 
  • #16
i get it AC^ = AB^ + BC^ :)
 
  • #17
no i stll don't get it:(
 
  • #18
Why do you use the sides of some unknown triangle, when you have a number for the lengths of the sides?
 
  • #19
lakitu said:
no i stll don't get it:(
Uhmm, I suggest you reading your textbook again. There should be some chapter about the distance betweeen 2 points in Cartesian coordinate. The distance between 2 points P(xP, yP), and Q(xQ, yQ) is:
d = PQ = \sqrt{(x_P - x_Q) ^ 2 + (y_P - y_Q) ^ 2}.
Now apply this, adn see if you can work out r = 3 \sqrt{2}.
Remember that the origin O is (0, 0).
Can you go from here? :)
 
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  • #20
lakitu said:
i get it AC^ = AB^ + BC^ :)

You were on the right track with this. If you have a point, (3, 3), you can use this theorem to work out the length of the hypotenuse, which is the distance between (3, 3) and the origin.
 
  • #21
lakitu, maybe you are not visualising well. Hope this image helps.

http://img72.imageshack.us/img72/2572/radial7nd.gif
 
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