HallsofIvy said:Why are you squaring? This will give you a relation between [itex]x^2[/itex] and [itex]y^2[/itex], not x and y, and so not the original equation. Just replace "x" with [itex]r cos(\theta)[/itex] and "y" with [itex]r sin(\theta)[/itex] in the original equations.
A polar equation is a mathematical expression that describes a curve or shape in polar coordinates, where a point is represented by its distance from the origin and its angle with respect to a fixed direction.
To convert a Cartesian equation to a polar equation, you can use the following substitutions: x = r cosθ and y = r sinθ. Once you have substituted these values, you can rearrange the equation to solve for r in terms of θ.
The value of r in a polar equation represents the distance from the origin to a point on the curve, also known as the radius. This distance is measured in the same units as the x and y axes in a Cartesian coordinate system.
To graph a polar equation, you can plot points by substituting different values of θ into the equation and calculating the corresponding values of r. These points can then be connected to create a curve. You can also use a graphing calculator to plot the equation.
Some common polar equations include circles, cardioids, roses, limaçons, lemniscates, and spirals. These equations can have different forms and parameters, but they all follow the same basic principles of polar coordinates.