Coordinate Conversion Worksheets Grade 12

1. A point P is located in the complex plane at coordinates (3, -4). Convert this rectangular coordinate representation to polar form (r, θ), where r ≥ 0 and θ is measured in radians between 0 and 2π. Express your answer in exact form where possible.
2. Convert the rectangular coordinates (-7, 7√3) to polar form (r, θ) where r > 0 and 0 ≤ θ < 2π.
3. A radar station tracks an aircraft at point P on its screen, which is a Cartesian grid overlaid on the display. The aircraft is located at rectangular coordinates (-7, -7√3). Convert this rectangular coordinate representation to polar form (r, θ), where r ≥ 0 and θ is measured in radians between 0 and 2π. Express your answer in exact form.

…and 4 more problems

1. Liam is designing a navigation system for a drone that needs to fly from its current position at coordinates (4, -4√3) to a charging station located at the origin. To program the drone's flight path, he needs to convert the rectangular coordinates of its current position to polar coordinates (r, θ) where r ≥ 0 and 0 ≤ θ < 2π. What polar coordinates should Liam use for the drone's programming?
2. Liam is designing a drone navigation system that uses polar coordinates. His drone is currently positioned at the point (4, -4√3) in the rectangular coordinate system. To program the drone's movement, he needs to convert this position to polar coordinates (r, θ) where r > 0 and 0 ≤ θ < 2π. What are the polar coordinates of the drone's position?
3. A navigation system tracks a ship's position on a radar screen. The ship is located at rectangular coordinates (12, -16) relative to the lighthouse at the origin, where coordinates are measured in kilometers. Convert these rectangular coordinates to polar coordinates (r, θ), where r ≥ 0 and θ is measured in radians between 0 and 2π. Express r as an exact value and θ as an exact radian measure.

…and 5 more problems

1. Liam is analyzing the position of a drone flying over a city grid. The drone's coordinates are recorded as (4, -4√3) meters from the control center. To program the drone's return path using polar navigation, Liam needs to convert these rectangular coordinates to polar form (r, θ), where r ≥ 0 and θ is measured in radians between 0 and 2π. What are the polar coordinates of the drone's position?
2. Convert the rectangular coordinates (-2, 2) to polar form (r, θ) where r > 0 and 0 ≤ θ < 2π.
3. A point P is located in the complex plane at coordinates (3, 4). Convert this rectangular coordinate representation to polar form (r, θ), where r ≥ 0 and θ is measured in radians between 0 and 2π. Express your answer in exact form where possible.

…and 3 more problems