8.2 Graphs of Polar Equations

Front

What is a limacon?

Back

A limacon is a type of polar graph that can have an inner loop, a dimple, or be a simple loop, depending on the parameters in its equation.

Front

What is a rose curve?

Back

A rose curve is a polar graph that resembles a flower and is defined by the equation r = a sin(nθ) or r = a cos(nθ), where n determines the number of petals.

Front

What is a cardioid?

Back

A cardioid is a specific type of limacon that has a single cusp and is represented by the polar equation r = 1 + sin(θ) or r = 1 + cos(θ).

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 from the positive x-axis.

Front

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

Back

The equation r = 1 + cos(θ) represents a limacon without an inner loop.

Front

What does the equation r = 1 - 3cos(θ) represent?

Back

The equation r = 1 - 3cos(θ) represents a limacon with an inner loop.

Front

What is the significance of the angle θ in polar coordinates?

Back

The angle θ in polar coordinates indicates the direction of the point from the origin, measured counterclockwise from the positive x-axis.

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 polar equation for a circle centered at the origin?

Back

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

Front

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

Back

The polar equation for a line at an angle θ is given by θ = constant.