AP PreCalc 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 (the polar axis).

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

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

Back

The polar coordinate (0, 0) represents the origin in both polar and rectangular coordinates.

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

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

Back

Front

What is the rectangular coordinate of the polar point (4, 3π/2)?

Back

The rectangular coordinates of (4, 3π/2) are (0, -4).

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 polar coordinate for the point (3, 3√3)?

Back

Front

How do you express the point (2, π/6) in rectangular coordinates?

Back

The rectangular coordinates are (2 * cos(π/6), 2 * sin(π/6)) = (√3, 1).

Front

What is the polar coordinate for the point (-3, 3√3)?

Back

The polar coordinate (-3, 3√3) indicates a point in the opposite direction of (3, 3√3) with the same angle.