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rsaad said:
Polar coordinates are a method of representing points in a 2-dimensional coordinate system using a distance from the origin and an angle from a reference line. This is in contrast to the more commonly used Cartesian coordinates, which use the distance from the origin along two perpendicular axes.
To convert from Cartesian coordinates (x,y) to polar coordinates (r,θ), you can use the following formulas:
r = √(x² + y²)
θ = tan⁻¹(y/x)
Note that for θ, you may need to adjust the value based on which quadrant the point is in.
The second equation in polar coordinates, also known as the polar equation, is used to represent curves and shapes in the polar coordinate system. It relates the distance (r) and angle (θ) values to create a graph in the shape of a spiral or circle.
To plot a point in polar coordinates, you will need to use the distance (r) and angle (θ) values to determine the location of the point on the polar grid. Start at the origin, then move r units in the direction of θ. The resulting point will be the plotted point in polar coordinates.
Polar coordinates can be used to solve geometry problems involving curves and shapes that are difficult to represent using Cartesian coordinates. By using the polar equation and the conversion formulas, you can easily find the distance and angle values for a given point on the curve or shape, making it easier to solve problems involving these types of shapes.
