Graphing Polar equations

Front

What is the polar coordinate system?

Back

A system where each point on a plane is determined by a distance from a reference point (the pole) and an angle from a reference direction.

Front

What is the equation of a line in polar coordinates?

Back

The equation can be expressed as \( \theta = \text{constant} \) or \( r = \text{constant} \) depending on the orientation.

Front

What is a cardioid in polar coordinates?

Back

A cardioid is a heart-shaped curve represented by the equation \( r = 1 + \sin(\theta) \) or \( r = 1 + \cos(\theta) \).

Front

What does the equation \( r = a + b \sin(\theta) \) represent?

Back

This represents a limacon, which can have an inner loop if \( b > a \).

Front

What is the significance of the angle \( \theta \) in polar coordinates?

Back

The angle \( \theta \) determines the direction of the point from the pole.

Front

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

Back

The polar equation is \( r = a \), where \( a \) is the radius.

Front

How do you convert polar coordinates to Cartesian coordinates?

Back

Use the formulas: \( x = r \cos(\theta) \) and \( y = r \sin(\theta) \).

Front

What is the polar equation for a rose curve?

Back

The polar equation is \( r = a \sin(n\theta) \) or \( r = a \cos(n\theta) \), where \( n \) determines the number of petals.

Front

What is the equation for a spiral of Archimedes?

Back

The equation is \( r = a + b\theta \), where \( a \) and \( b \) are constants.

Front

What is the polar equation for a lemniscate?

Back

The polar equation is \( r^2 = a^2 \cos(2\theta) \) or \( r^2 = a^2 \sin(2\theta) \).