Polar Coordinates

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

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

Back

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

Front

Convert the polar coordinates (6, 2π/3) to rectangular form.

Back

(-3, 3√3)

Front

What is the formula to convert rectangular coordinates (x, y) to polar coordinates (r, θ)?

Back

Use the formulas: r = √(x² + y²) and θ = arctan(y/x).

Front

Convert the rectangular coordinates (4, 4) to polar form (r, θ).

Back

(4√2, π/4)

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 the radius r in polar coordinates?

Back

The radius r represents the distance from the origin to the point in the polar coordinate system.

Front

Convert the polar coordinates (3, 3π/4) to rectangular form.

Back

(-3√2/2, 3√2/2)

Front

Which point represents the polar coordinates (-4, π/2)?

Back

The point is located at (0, -4) in rectangular coordinates.

Front

What is the relationship between polar coordinates and Cartesian coordinates?

Back

Polar coordinates provide an alternative way to represent points in a plane, while Cartesian coordinates use (x, y) pairs.