identifying polar graphs

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 polar equation for a circle centered at the pole with radius r?

Back

The polar equation is r = k, where k is the radius of the circle.

Front

What does the equation r = a cos(θ) represent?

Back

It represents a circle centered on the polar axis with radius a/2.

Front

What does the equation r = a sin(θ) represent?

Back

It represents a circle centered on the line θ = π/2 with radius a/2.

Front

What is the general form of a rose curve in polar coordinates?

Back

The general form is r = a sin(nθ) or r = a cos(nθ), where n determines the number of petals.

Front

How do you determine the number of petals in a rose curve given by r = a sin(nθ)?

Back

If n is odd, the number of petals is n. If n is even, the number of petals is 2n.

Front

What is the polar equation for a line through the pole at an angle θ?

Back

The polar equation is θ = constant.

Front

What does the equation r = a + b cos(θ) represent when a and b are equal?

Back

It represents a cardioid.

Front

What is the difference between r = a + b sin(θ) and r = a + b cos(θ)?

Back

The difference lies in the orientation of the graph; sin(θ) shifts the graph vertically, while cos(θ) shifts it horizontally.

Front

What is the polar equation for a limaçon with an inner loop?

Back

The polar equation is r = a + b cos(θ) or r = a + b sin(θ) where |b| > |a|.