Polar Coordinates

Front

What are polar coordinates?

Back

A system of coordinates where each point is determined by a distance from a reference point (the origin) and an angle from a reference direction.

Front

How do you convert polar coordinates to rectangular form?

Back

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

Front

What is the ordered pair format for polar coordinates?

Back

(r, θ)

Front

What is the polar coordinate for the rectangular point (-3, 0)?

Back

(3, π) because the distance is 3 and the angle is π.

Front

What is the polar coordinate for the rectangular point (0, 3)?

Back

(3, π/2) because the distance is 3 and the angle is π/2.

Front

Convert the polar coordinates (6, 2π/3) to rectangular form.

Back

(-3, 3√3) using x = r * cos(θ) and y = r * sin(θ).

Front

What does 'r' represent in polar coordinates?

Back

The distance from the origin to the point.

Front

What does 'θ' represent in polar coordinates?

Back

The angle measured from the positive x-axis to the line connecting the origin to the point.

Front

How do you find the angle θ for a point in the second quadrant?

Back

θ = π - θ' where θ' is the reference angle.

Front

How do you find the angle θ for a point in the third quadrant?

Back

θ = θ' + π where θ' is the reference angle.