Polar Graphs

Front

What is a polar graph?

Back

A polar graph is a two-dimensional graph that represents points in terms of their 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 = 4 represent in polar coordinates?

Back

It represents a circle with a radius of 4 centered at the origin.

Front

What is a limacon in polar coordinates?

Back

A limacon is a type of polar curve that resembles a distorted circle and can have an inner loop, be dimpled, or be convex.

Front

What distinguishes an inner loop limacon from a dimpled limacon?

Back

An inner loop limacon has a loop that goes inside the curve, while a dimpled limacon has a dimple but no inner loop.

Front

What is the significance of the coefficient in r = a + b cos(θ)?

Back

The coefficient determines the size and shape of the limacon; if a < b, it forms an inner loop.

Front

How do you identify a dimpled limacon?

Back

A dimpled limacon can be identified when the equation is of the form r = a + b cos(θ) or r = a + b sin(θ) with a < b.

Front

What is the polar equation for a circle centered at the pole?

Back

The polar equation for a circle centered at the pole is r = a, where a is the radius.

Front

What does the equation r = 1 + cos(θ) represent?

Back

It represents a dimpled limacon with a maximum radius of 2 and a minimum radius of 1.

Front

How do you convert a polar equation to Cartesian coordinates?

Back

To convert, use the relationships x = r cos(θ) and y = r sin(θ).