Polar graphing

Front

What is a polar graph?

Back

A polar graph is a graph that represents points in a plane using a distance from a reference point (the pole) and an angle from a reference direction (the polar axis).

Front

What is the general form of a polar equation?

Back

The general form of a polar equation is r = f(Θ), where r is the distance from the origin and Θ is the angle.

Front

What does the equation r = a + bcos(Θ) represent?

Back

This equation represents a limacon, which can have an inner loop, a dimple, or be a cardioid depending on the values of a and b.

Front

What is the significance of the coefficient in front of cos(Θ) or sin(Θ) in polar equations?

Back

The coefficient determines the size and shape of the graph. For example, larger coefficients result in larger loops or petals.

Front

What is the equation for a circle in polar coordinates?

Back

The equation for a circle centered at the pole with radius a is r = a.

Front

How do you convert polar coordinates to Cartesian coordinates?

Back

To convert polar coordinates (r, Θ) to Cartesian coordinates (x, y), use the formulas: x = r * cos(Θ) and y = r * sin(Θ).

Front

What is the relationship between the angle Θ and the direction of the graph in polar coordinates?

Back

The angle Θ determines the direction of the point from the origin; it is measured counterclockwise from the positive x-axis.

Front

What is a limacon with an inner loop?

Back

A limacon with an inner loop occurs when the absolute value of b is greater than a in the equation r = a + bcos(Θ) or r = a + bsin(Θ).

Front

What is the effect of changing the sign of r in polar equations?

Back

Changing the sign of r reflects the graph across the origin.

Front

What is the diameter of the outer loop in the limacon r = 3 - 5cos(Θ)?

Back

The diameter of the outer loop is 8.