Distance between two points in polar coordinate system.

In summary, the conversation discusses ideas on how to calculate distance between two points in Polar coordinate system without converting to Cartesian. One suggestion is to use the law of cosines and construct a triangle with vertices at the origin and the two points. However, this method can be tedious for calculating inverse square laws in polar/spherical coordinates. Further elaboration can be given if needed.
  • #1
sotnet
3
0
Guys,

Any ideas on how to calculate distance between two points in Polar coordinate system without converting their coordinates to Cartesian?

Ps. I know that if I converted from Polar (r, t) to Cartesian (x, y) by x = r.cos(t), y = r.sin(t), then the distance between two points would be d = sqrt((x1 - x2)^2 + (y1 - y2)^2).Thanks,
Steve
 
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  • #2
You use the law of cosines.
Construct a triangle with vertices at the origin, and the two points.
Its a cool trick, but makes for a huge pain in the ass for calculating inverse square laws etc. in polar/spherical.

I can elaborate if the setup doesn't make sense.
 

What is the formula for finding the distance between two points in polar coordinate system?

The distance between two points in the polar coordinate system can be found using the formula: d = √(r1² + r2² - 2r1r2cos(θ1 - θ2)), where r1 and r2 are the radii of the two points and θ1 and θ2 are the corresponding angles.

How do you convert polar coordinates to Cartesian coordinates?

To convert polar coordinates (r, θ) to Cartesian coordinates (x, y), the following formulas can be used: x = rcos(θ) and y = rsin(θ). These formulas use the trigonometric functions cosine and sine to determine the x and y coordinates.

Can the distance between two points in polar coordinate system be negative?

No, the distance between two points in any coordinate system cannot be negative. It represents the length of the line segment connecting the two points, which is always a positive value.

What is the difference between polar and Cartesian coordinate systems?

The polar coordinate system uses a distance and angle to represent a point, while the Cartesian coordinate system uses x and y coordinates to represent a point. The polar coordinate system is often used for describing circular and curved shapes, while the Cartesian coordinate system is used for describing straight lines and shapes.

Is it possible to find the distance between two points in polar coordinate system using only the angle?

No, the distance between two points cannot be determined using only the angle in the polar coordinate system. The distance is also dependent on the radii of the two points. Both the angle and the radii are needed to calculate the distance between two points in the polar coordinate system.

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