# What is Cartesian and polar coordinates?

## What is Cartesian and polar coordinates?

This leads to an important difference between Cartesian coordinates and polar coordinates. In Cartesian coordinates there is exactly one set of coordinates for any given point. In polar coordinates there is literally an infinite number of coordinates for a given point.

## What is Cartesian to polar?

To convert from Cartesian coordinates to polar coordinates: r=√x2+y2 . Since tanθ=yx, θ=tan−1(yx) . So, the Cartesian ordered pair (x,y) converts to the Polar ordered pair (r,θ)=(√x2+y2,tan−1(yx)) .

How do you convert Cartesian coordinates to polar coordinates?

To convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y) :

1. x = r × cos( θ )
2. y = r × sin( θ )

What are Cartesian coordinates used for?

Cartesian coordinates can be used not only to specify the location of points, but also to specify the coordinates of vectors. The Cartesian coordinates of two or three-dimensional vectors look just like those of points in the plane or three-dimensional space.

### How do you convert Cartesian to polar in Matlab?

pol2cart (MATLAB Functions) [X,Y] = pol2cart(THETA,RHO) transforms the polar coordinate data stored in corresponding elements of THETA and RHO to two-dimensional Cartesian, or xy, coordinates. The arrays THETA and RHO must be the same size (or either can be scalar). The values in THETA must be in radians.

### How do you convert Cartesian to polar formula?

Cartesian to Polar Conversion Formulas r2 = x2 +y2 r = √x2+y2 θ = tan−1(y x) r 2 = x 2 + y 2 r = x 2 + y 2 θ = tan − 1 (y x) Let’s work a quick example. Example 1 Convert each of the following points into the given coordinate system.

What is a point in polar coordinates and Cartesian coordinates?

When we know a point in Polar Coordinates (r, θ), and we want it in Cartesian Coordinates (x,y) we solve a right triangle with a known long side and angle: Example: What is (13, 22.6°) in Cartesian Coordinates? Answer: the point (13, 22.6°) is almost exactly (12, 5) in Cartesian Coordinates.

How do you find the polar coordinate of a graph?

Common Polar Coordinate Graphs 1 θ = β . We can see that this is a line by converting to Cartesian coordinates as follows θ = β tan − 1(y x) = β y x 2 rcosθ = a This is easy enough to convert to Cartesian coordinates to x = a. So, this is a vertical line. 3 rsinθ = b Likewise, this converts to y = b and so is a horizontal line.

#### How do you convert 2x-5×3 to polar coordinates?

Convert 2x −5×3 = 1+xy 2 x − 5 x 3 = 1 + x y into polar coordinates. θ into Cartesian coordinates. a Convert 2x−5×3 =1 +xy 2 x − 5 x 3 = 1 + x y into polar coordinates. Show Solution

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