Polar coordinates are a mathematical system used to describe the position of a point in a two-dimensional plane. They are different from Cartesian coordinates in that they use a distance and angle from the origin as the coordinates, rather than x and y values.
To convert from polar to Cartesian coordinates, you can use the following formulas: x = r * cos(θ) and y = r * sin(θ), where r is the distance from the origin and θ is the angle from the positive x-axis. To convert from Cartesian to polar coordinates, you can use the formulas: r = √(x^2 + y^2) and θ = arctan(y/x).
The formula for finding the distance between two points using polar coordinates is d = √(r1^2 + r2^2 - 2r1r2cos(θ2 - θ1)), where r1 and r2 are the distances from the origin to the two points and θ1 and θ2 are the angles from the positive x-axis to the two points.
To find the angle between two points using polar coordinates, you can use the formula θ = arctan((y2 - y1)/(x2 - x1)), where (x1, y1) and (x2, y2) are the coordinates of the two points.
To solve for the distance between two points on a graph, you can first plot the points on a polar coordinate system. Then, use the distance formula (d = √(r1^2 + r2^2 - 2r1r2cos(θ2 - θ1))) to calculate the distance between the two points.