Polar coordinates

Front

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

Back

x = rcosθ, y = rsinθ

Front

What is the polar coordinate representation of the point (0, 3)?

Back

(3, π/2)

Front

How do you find the angle θ in polar coordinates when given a point (x, y)?

Back

θ = arctan(y/x) for x ≠ 0.

Front

What is the polar coordinate representation of the point (-3, 0)?

Back

(3, π) because the radius is positive.

Front

What does the polar coordinate (r, θ) represent geometrically?

Back

A point in the plane defined by a distance r from the origin and an angle θ from the positive x-axis.

Front

How do you convert the rectangular coordinates (x, y) = (3, 3) to polar coordinates?

Back

r = √(x² + y²) = √(3² + 3²) = 3√2; θ = arctan(3/3) = π/4, so (3√2, π/4).

Front

What is the significance of a negative radius in polar coordinates?

Back

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

Front

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

Back

E, as it corresponds to the angle and distance from the origin.

Front

How do you determine the quadrant of a point given in polar coordinates?

Back

By analyzing the angle θ: 0 to π/2 is Quadrant I, π/2 to π is Quadrant II, π to 3π/2 is Quadrant III, and 3π/2 to 2π is Quadrant IV.

Front

What is the relationship between polar coordinates and the unit circle?

Back

Polar coordinates can be visualized on the unit circle where r is the radius and θ is the angle.