- #1
A polar equation is a mathematical expression that relates the distance and angle of a point in a polar coordinate system. It is used to graph curves and shapes in a two-dimensional plane.
A polar equation uses polar coordinates, which are based on a system of angles and distances from the origin, while a Cartesian equation uses rectangular coordinates, which are based on a system of x and y coordinates. In a polar equation, the distance from the origin is represented by the variable r, and the angle is represented by the variable θ.
To sketch a polar equation, you first need to plot points on a polar coordinate system by substituting values of θ into the equation and solving for r. Then, you can connect the points to create a curve or shape. You may also need to adjust the scale of the axes to ensure that the graph fits on the page.
A polar equation in the form of r = f(θ) represents a curve with a fixed distance from the origin at a given angle θ. This type of equation is useful for graphing circles, ellipses, and other symmetric shapes.
To convert a Cartesian equation to a polar equation, you can use the following formulas:
x = r cos(θ) and y = r sin(θ). Substitute these values into the Cartesian equation and simplify to get the polar equation in terms of r and θ.