Polar and cartesian coordinates

In summary, polar coordinates use a distance and angle to describe a location, while cartesian coordinates use an x and y coordinate system. To convert from polar to cartesian coordinates, use the formulas x = r * cos(theta) and y = r * sin(theta). Both polar and cartesian coordinates can represent any point, but they are often used for different purposes - polar for direction and distance, cartesian for mathematics and engineering. To graph points, the distance and angle are plotted in polar coordinates, while the x and y coordinates are plotted in cartesian coordinates.
  • #1
lmannoia
32
0

Homework Statement


Write the following polar equation in Cartesian coordinates:
r= 2/(3cos(theta)-9sin(theta))


Homework Equations


r = (x^2 + y^2) ^.5
x=rcos theta
y=rsin theta
sin^2(x)+cos^2(x) = 1


The Attempt at a Solution


I'm stuck on how to do this. Any push in the right direction would be appreciated greatly!
 
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  • #2
Clear that fraction by multiplying both sides by 3cos(theta)- 9sin(theta) to get
r(3cos(theta)- 9sin(theta))= 3 (r cos(theta))- 9(r sin(theta))= 2.

Now it should be obvious.
 
  • #3
Wow, I can't believe that I didn't see that. Thanks a lot!
 

1. What is the difference between polar and cartesian coordinates?

Polar coordinates use a distance and angle from a fixed point to describe a location, while cartesian coordinates use an x and y coordinate system to describe a location.

2. How do you convert polar coordinates to cartesian coordinates?

To convert from polar coordinates to cartesian coordinates, use the following formulas: x = r * cos(theta) and y = r * sin(theta), where r is the distance and theta is the angle.

3. Can any point be represented in both polar and cartesian coordinates?

Yes, any point can be represented in both polar and cartesian coordinates, as they are two different ways of describing the same location.

4. Are polar and cartesian coordinates used for different purposes?

Yes, polar coordinates are often used in situations where direction and distance are more important, such as in navigation or physics, while cartesian coordinates are more commonly used in mathematics and engineering.

5. How do you graph points in polar and cartesian coordinates?

In polar coordinates, the distance from the origin is plotted on the x-axis and the angle is plotted on the y-axis. In cartesian coordinates, the x and y coordinates are plotted on the x and y axes, respectively.

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