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 is a cardioid in polar coordinates?

Back

A cardioid is a heart-shaped curve represented by the polar equation r = a + b cos(θ) or r = a + b sin(θ), where a and b are positive constants.

Front

What is a limacon?

Back

A limacon is a type of polar curve that can have an inner loop, be dimpled, or be convex, represented by equations of the form r = a + b cos(θ) or r = a + b sin(θ).

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

How do you determine the number of petals in a rose curve?

Back

If n is odd, the rose curve has n petals. If n is even, the rose curve has 2n petals.

Front

What is the significance of the coefficients in polar equations?

Back

The coefficients in polar equations affect the size and shape of the graph, with larger coefficients resulting in larger curves.

Front

What is the difference between a convex limacon and an inner loop limacon?

Back

A convex limacon has no inner loop and is shaped like a rounded curve, while an inner loop limacon has a loop that goes inside the curve.

Front

What does the term 'polar axis' refer to?

Back

The polar axis is the reference line from which angles are measured in polar coordinates, typically aligned with 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).