#4 coordinate graph how to#

Polar equations may be graphed by making a table of values for and.

If an equation fails a symmetry test, the graph may or may not exhibit symmetry.

There are three symmetry tests that indicate whether the graph of a polar equation will exhibit symmetry.

It is easier to graph polar equations if we can test the equations for symmetry with respect to the line the polar axis, or the pole.

For example, suppose we are given the equation We replace with to determine if the new equation is equivalent to the original equation. In the first test, we consider symmetry with respect to the line ( y-axis). Further, we will use symmetry (in addition to plotting key points, zeros, and maximums of to determine the graph of a polar equation.

#4 coordinate graph how to#

By performing three tests, we will see how to apply the properties of symmetry to polar equations. If an equation has a graph that is symmetric with respect to an axis, it means that if we folded the graph in half over that axis, the portion of the graph on one side would coincide with the portion on the other side. Symmetry is a property that helps us recognize and plot the graph of any equation.

Recall that the coordinate pair indicates that we move counterclockwise from the polar axis (positive x-axis) by an angle of and extend a ray from the pole (origin) units in the direction of All points that satisfy the polar equation are on the graph.

Just as a rectangular equation such as describes the relationship between and on a Cartesian grid, a polar equation describes a relationship between and on a polar grid.