Converting Polar Coordinates

Front

Convert the polar coordinates (r, θ) to rectangular coordinates (x, y).

Back

x = rcos(θ), y = rsin(θ)

Front

What is the formula to convert from rectangular coordinates (x, y) to polar coordinates (r, θ)?

Back

r = √(x² + y²), θ = arctan(y/x)

Front

Convert the polar coordinates (1, π/2) to rectangular coordinates.

Back

(0, 1)

Front

Convert the polar coordinates (5, 0) to rectangular coordinates.

Back

(5, 0)

Front

What is the value of r when converting the point (-3, 3√3) to polar coordinates?

Back

r = √((-3)² + (3√3)²) = 6

Front

What is the angle θ in radians for the point (0, -4) in polar coordinates?

Back

θ = 3π/2

Front

Convert the rectangular coordinates (-4, 4) to polar coordinates.

Back

(4√2, 3π/4)

Front

What is the rectangular coordinate for the polar point (4, π)?

Back

(-4, 0)

Front

Convert the polar coordinates (6, 5π/4) to rectangular coordinates.

Back

(-3√2, -3√2)

Front

What is the relationship between the angle θ and the coordinates in polar form?

Back

θ is the angle measured from the positive x-axis.