Converting Polar and Rectangular

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

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

Back

Use the formulas: x = r * cos(θ) and y = r * sin(θ).

Front

What is the relationship between rectangular coordinates (x, y) and polar coordinates (r, θ)?

Back

The relationship is given by: r = √(x² + y²) and θ = tan⁻¹(y/x).

Front

Convert the polar coordinates (3, π/4) to rectangular form.

Back

(3 * cos(π/4), 3 * sin(π/4)) = (3√2/2, 3√2/2).

Front

What is the polar coordinate of the point (0, 0) in rectangular coordinates?

Back

The polar coordinate is (0, θ) for any angle θ.

Front

Back

Front

What is the polar coordinate of the point (2, 2) in rectangular coordinates?

Back

The polar coordinates are (2√2, π/4).

Front

Back

Front

What is the polar coordinate of the point (-3, 0) in rectangular coordinates?

Back

The polar coordinates are (3, π).

Front

Back