A polar equation is a mathematical expression that describes a relationship between a point on a polar coordinate system and its distance from the pole (origin) and angle from the polar axis.
To convert a polar equation to a Cartesian equation, you can use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
where r is the distance from the origin and θ is the angle from the positive x-axis.
To graph a polar equation, you can plot points by substituting different values for r and θ and then connecting them. You can also use a graphing calculator or online graphing tool to plot the equation.
The polar axis is the horizontal line that passes through the pole in a polar coordinate system. It represents the x-axis in a Cartesian coordinate system and is used to measure the angle (θ) in a polar equation.
To identify the graph of a polar equation, you can look at the equation and determine its symmetry, number of petals, and the location of any vertical or horizontal lines of symmetry. You can also plot points or use a graphing calculator to visualize the graph.