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 rectangular coordinates (x, y) to polar coordinates (r, θ)?

Back

To convert (x, y) to (r, θ): r = √(x² + y²) and θ = arctan(y/x).

Front

What is the relationship between polar coordinates and Cartesian coordinates?

Back

Polar coordinates (r, θ) can be converted to Cartesian coordinates (x, y) using the formulas: x = r * cos(θ) and y = r * sin(θ).

Front

What does the 'r' represent in polar coordinates?

Back

In polar coordinates, 'r' represents the radial distance from the origin (pole) to the point.

Front

What does the 'θ' represent in polar coordinates?

Back

In polar coordinates, 'θ' represents the angle measured from the positive x-axis to the line connecting the origin to the point.

Front

How do you determine the angle θ in polar coordinates?

Back

The angle θ can be determined using the arctangent function: θ = arctan(y/x), adjusting for the quadrant of the point.

Front

What is the polar coordinate for the point (0, 0) in Cartesian coordinates?

Back

The polar coordinate for the point (0, 0) is (0, θ) for any angle θ.

Front

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

Back

To convert (r, θ) to (x, y): x = r * cos(θ) and y = r * sin(θ).

Front

What is the polar coordinate for the point (1, π/4)?

Back

The rectangular coordinates for (1, π/4) are (√2/2, √2/2).

Front

What is the significance of the angle θ being greater than 2π in polar coordinates?

Back

An angle θ greater than 2π represents a full rotation plus additional angle, effectively wrapping around the circle.