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

Back

This equation represents a cardioid shape in polar coordinates.

Front

What is the significance of the polar axis in polar graphs?

Back

The polar axis is the horizontal line from the pole (origin) to the right, serving as a reference for measuring angles.

Front

How do you determine the symmetry of a polar graph?

Back

A polar graph is symmetric about the polar axis if replacing θ with -θ yields the same equation.

Front

What is the maximum r-value in the equation r = 1 - 2sin(θ)?

Back

The maximum r-value is 1, occurring when sin(θ) = -1.

Front

What does the equation r = 2 represent?

Back

This equation represents a circle with a radius of 2 centered at the pole.

Front

What is the general form of a polar equation?

Back

The general form of a polar equation can be expressed as r = f(θ), where f is a function of θ.

Front

What is the relationship between polar and Cartesian coordinates?

Back

The relationship is given by x = r cos(θ) and y = r sin(θ).

Front

What does the equation r = 6 + 6sin(θ) represent?

Back

This equation represents a limacon with an inner loop in polar coordinates.

Front

How do you find the angle θ for a given polar equation?

Back

To find θ, set r to a specific value and solve the polar equation for θ.