8.2 Graphs of Polar Equations

Front

What is a polar equation?

Back

A polar equation is an equation that expresses the relationship between the radius (r) and the angle (θ) in a polar coordinate system.

Front

What is a limacon?

Back

A limacon is a type of polar curve that can have an inner loop, be dimpled, or be a convex shape, depending on the coefficients in the equation.

Front

Identify the polar equation: r = 1 - 3cosθ.

Back

Limacon with inner loop.

Front

What is the general form of a dimpled limacon?

Back

The general form of a dimpled limacon is r = a + b cos(θ) or r = a + b sin(θ) where a < b.

Front

Identify the polar equation: r = 3 + 2cosθ.

Back

This is an equation for a dimpled limacon.

Front

What is the polar equation for a circle centered at the origin with radius 3?

Back

The polar equation is r = 3.

Front

Identify the polar equation for a circle with radius 3 centered at the x-axis.

Back

The polar equation is r = 3cos(θ).

Front

What is the maximum r-value of the polar equation r = 4sin(2θ)?

Back

The maximum r-value is 4.

Front

Identify the polar equation with a maximum r-value of 8.

Back

The equation is r = -2 + 6sin(θ).

Front

What is the polar equation for a rose curve with 8 petals?

Back

The polar equation is r = cos(8θ).