Polar

Front

What are polar coordinates?

Back

Polar coordinates are a two-dimensional coordinate system 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 relationship between polar and Cartesian coordinates?

Back

The relationship is given by the equations: x = r * cos(θ) and y = r * sin(θ), where (r, θ) are polar coordinates and (x, y) are Cartesian coordinates.

Front

How do you convert polar coordinates (r, θ) to Cartesian coordinates (x, y)?

Back

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

Front

What does the angle θ represent in polar coordinates?

Back

The angle θ represents the counterclockwise angle from the positive x-axis to the line connecting the origin to the point.

Front

What is the significance of a negative radius in polar coordinates?

Back

A negative radius indicates that the point is in the opposite direction of the angle θ.

Front

How do you represent the point (3, 3π/4) in Cartesian coordinates?

Back

x = 3 * cos(3π/4) = -3/√2, y = 3 * sin(3π/4) = 3/√2.

Front

What is the polar coordinate representation of the origin?

Back

The origin is represented as (0, θ) for any angle θ.

Front

How do you convert the polar equation r = 7 to rectangular form?

Back

The rectangular form is x² + y² = 49.

Front

What is the polar coordinate for the point directly to the left of the origin?

Back

The polar coordinate is (-r, θ) where r is the distance from the origin and θ is any angle.

Front

What is the polar coordinate for the point (2, π/6)?

Back

In Cartesian coordinates, this point is (√3, 1).