Polar Coordinates and Equations

Front

What are polar coordinates?

Back

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

Front

What is the general form of a polar equation?

Back

r = f(θ), where r is the radius and θ is the angle.

Front

How do you convert polar coordinates to Cartesian coordinates?

Back

Use the formulas: x = r * cos(θ) and y = r * sin(θ).

Front

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

Back

It represents the direction of the point from the pole, measured counterclockwise from the positive x-axis.

Front

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

Back

It represents a polar graph that can create various shapes depending on the values of a and b.

Front

What is the polar coordinate for the point (3, 3π/4)?

Back

The point is located 3 units from the pole at an angle of 3π/4 radians.

Front

What is the polar coordinate for the point (-4, -2π/3)?

Back

The point is located 4 units from the pole at an angle of -2π/3 radians, which is equivalent to 4 units in the opposite direction.

Front

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

Back

r = a, where a is the radius of the circle.

Front

What does the equation r = 4 sin(θ) represent?

Back

It represents a circle with a radius of 2, centered at (0, 2) in Cartesian coordinates.

Front

How do you identify the graph of r = 6 sin(2θ)?

Back

It represents a rose curve with 4 petals, since the coefficient of θ is 2.