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 origin) and an angle from a reference direction.

Front

What is the relationship between polar coordinates and rectangular coordinates?

Back

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

Front

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

Back

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

Front

What is the significance of the angle in polar coordinates?

Back

The angle θ in polar coordinates indicates the direction of the point from the origin, measured counterclockwise from the positive x-axis.

Front

What does the radius (r) represent in polar coordinates?

Back

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

Front

How do you determine the quadrant of a point given in polar coordinates?

Back

The quadrant can be determined by the angle θ: 0 to π/2 (1st quadrant), π/2 to π (2nd quadrant), π to 3π/2 (3rd quadrant), and 3π/2 to 2π (4th quadrant).

Front

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

Back

The polar coordinate for the point (0, 0) is (0, θ) for any angle θ, as it represents the origin.

Front

How do you represent negative radius in polar coordinates?

Back

A negative radius indicates the point is in the opposite direction of the angle. For example, (-r, θ) is equivalent to (r, θ + π).

Front

What is the polar coordinate for the point (4, 11π/6)?

Back

The polar coordinate (4, 11π/6) represents a point that is 4 units away from the origin, at an angle of 11π/6 radians.

Front

How do you find the angle for a point given in polar coordinates?

Back

The angle θ can be found directly from the polar coordinates (r, θ) as the second value.