Polar Coordinates and Graphs

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 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

How do you determine if two polar coordinates represent the same point?

Back

Two polar coordinates (r, θ) and (r', θ') represent the same point if r = r' and θ = θ' + 2kπ or r = -r' and θ = θ' + (2k+1)π for any integer k.

Front

What is the significance of the angle in polar coordinates?

Back

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

Front

What does a negative radius indicate in polar coordinates?

Back

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

Front

How do you find the distance between two points in polar coordinates?

Back

Front

What is the polar coordinate of the point (0, θ)?

Back

The polar coordinate (0, θ) represents the origin, regardless of the angle θ.

Front

How do you convert polar coordinates to rectangular coordinates?

Back

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

Front

What is the polar coordinate of the point (r, π)?

Back

The polar coordinate (r, π) represents a point that is r units away from the origin in the direction of the negative x-axis.

Front

What is the effect of adding 2π to the angle in polar coordinates?

Back

Adding 2π to the angle in polar coordinates does not change the point's location; it represents a full rotation.