Cartesian points in polar coordinates.

In summary, The problem is asking to express the Cartesian point (3, 3) in polar coordinates. Instead of using a calculator, it is recommended to draw a line segment from the origin to (3, 3) and determine the angle it makes with the positive x-axis. The radial component, or the distance from the origin to (3, 3), can be found using the formula r = √(x^2 + y^2). In this case, r = 3√2. The angle can be found using the formula a = atan(y/x), which in this case gives 45 degrees. Therefore, the polar coordinates for (3, 3) are (3√2, 45
  • #1
lakitu
27
0
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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  • #2
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?
 
  • #3
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
 
  • #4
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
 
  • #5
Look again at the radial component. How far is it from the origin to (3,3)?
 
  • #6
im not sure what you mean? i can only think the distance is 6 if its not 3 what i originally believed :)
 
  • #7
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 :)
 
  • #8
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 [tex]3\sqrt{2}[/tex].
 
  • #9
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 [tex]3\sqrt{2}[/tex].
 
  • #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 [tex]3\sqrt{2}[/tex] ?

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:
[tex]d = PQ = \sqrt{(x_P - x_Q) ^ 2 + (y_P - y_Q) ^ 2}[/tex].
Now apply this, adn see if you can work out [tex]r = 3 \sqrt{2}[/tex].
Remember that the origin O is (0, 0).
Can you go from here? :)
 
Last edited:
  • #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 [Broken]
 
Last edited by a moderator:

1. What are Cartesian points in polar coordinates?

Cartesian points in polar coordinates are a way of representing points in a two-dimensional space using two different coordinate systems. The first coordinate system, Cartesian coordinates, uses the x and y axes to plot points. The second coordinate system, polar coordinates, uses a distance (r) from the origin and an angle (θ) from a reference line to plot points.

2. How do you convert a point from Cartesian coordinates to polar coordinates?

To convert a point from Cartesian coordinates (x,y) to polar coordinates (r,θ), you can use the following equations: r = √(x^2 + y^2) and θ = arctan(y/x). This will give you the distance from the origin and the angle from the reference line, respectively.

3. What are the advantages of using polar coordinates over Cartesian coordinates?

One advantage of using polar coordinates is that they can be useful in describing circular or symmetrical patterns, as the distance and angle are directly related to the shape. They can also be easier to visualize and understand for certain applications, such as mapping out points on a radar screen.

4. Can you convert a point from polar coordinates to Cartesian coordinates?

Yes, you can convert a point from polar coordinates (r,θ) to Cartesian coordinates (x,y) using the following equations: x = r * cos(θ) and y = r * sin(θ). These equations use trigonometric functions to determine the x and y coordinates based on the distance and angle.

5. How are Cartesian and polar coordinates used in real-world applications?

Cartesian and polar coordinates are used in a variety of real-world applications, including navigation, astronomy, and engineering. They can be used to plot the location of objects, map out patterns, and solve mathematical equations. For example, GPS systems use both systems to pinpoint locations on a map, and astronomers use polar coordinates to plot the location of stars in the night sky.

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