Polar Coordinates

Front

What is the polar coordinate representation of a point?

Back

A point in polar coordinates is represented as (r, θ), where r is the distance from the origin and θ is the angle from the positive x-axis.

Front

How do you convert from polar coordinates to rectangular coordinates?

Back

To convert from polar to rectangular coordinates, use the formulas: x = r * cos(θ) and y = r * sin(θ).

Front

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

Back

The point (2, π/6) represents a point that is 2 units away from the origin at an angle of π/6 radians.

Front

What is the relationship between polar and rectangular coordinates?

Back

The relationship is defined by the equations: x = r * cos(θ) and y = r * sin(θ).

Front

What is the angle θ in polar coordinates?

Back

The angle θ is the angle measured from the positive x-axis to the line connecting the origin to the point.

Front

How do you write an ordered pair in polar coordinates?

Back

An ordered pair in polar coordinates is written as (r, θ).

Front

What is the equation for y in terms of polar coordinates?

Back

In polar coordinates, y = r * sin(θ).

Front

What is the equation for x in terms of polar coordinates?

Back

In polar coordinates, x = r * cos(θ).

Front

How do you convert from rectangular coordinates to polar coordinates?

Back

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

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.