Polar and Rectangular 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

What are rectangular coordinates?

Back

Rectangular coordinates (or Cartesian coordinates) represent a point in a two-dimensional space using an ordered pair (x, y), where x is the horizontal distance from the origin and y is the vertical distance.

Front

How do you convert polar coordinates to rectangular coordinates?

Back

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

Front

How do you convert rectangular coordinates to polar coordinates?

Back

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

Front

What is the significance of the angle in polar coordinates?

Back

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

Front

What does a negative radius in polar coordinates indicate?

Back

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

Front

What is the polar coordinate representation of the point (-2, -2)?

Back

The polar coordinate representation of the point (-2, -2) can be found by calculating the radius and angle, resulting in (r, θ) = (2√2, 5π/4) or other equivalent forms.

Front

How do you find equivalent polar coordinates?

Back

Equivalent polar coordinates can be found by adding or subtracting multiples of 2π to the angle while keeping the radius the same, or by negating both the radius and angle.

Front

What is the polar coordinate of the point (4, 4)?

Back

The polar coordinate of the point (4, 4) is (4√2, π/4).

Front

What is the rectangular form of the polar coordinates (6, 2π/3)?

Back

The rectangular form of the polar coordinates (6, 2π/3) is (-3, 3√3).