Coordinate Conversion Worksheets Grade 12

1. A marine biologist is tracking a dolphin that surfaces at position (5, -5√3) meters relative to her research boat. To plot the dolphin's location on her polar coordinate tracking system, she 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 polar coordinates should she record for the dolphin's position?
2. An engineer is designing a robotic arm that moves in a rectangular coordinate system. The arm's end effector needs to reach a point at coordinates (-5, 5√3) centimeters from the base. To program the arm's rotational movement, she needs to convert these rectangular coordinates to polar coordinates (r, θ) where r ≥ 0 and 0 ≤ θ < 2π. What polar coordinates should the engineer use?
3. Liam is designing a drone navigation system that uses polar coordinates. His drone is currently at the rectangular coordinates (4, -4√3) meters relative to its home base. To program the drone's return path, he needs to convert this position to polar coordinates (r, θ) where r ≥ 0 and 0 ≤ θ < 2π. What polar coordinates should Liam use for his drone's current position?

…and 5 more problems

1. A point P is located at coordinates (-5, 5√3) on the Cartesian plane. Convert this rectangular coordinate to polar form (r, θ), where r ≥ 0 and θ is measured in radians between 0 and 2π. Express your answer in exact form.
2. Liam is designing a drone navigation system that uses polar coordinates. His drone is currently at position (4, 4√3) in rectangular coordinates. To program the drone's flight path, he needs to convert this position to polar coordinates (r, θ) where r ≥ 0 and 0 ≤ θ < 2π. What polar coordinates should Liam use for his drone's current position?
3. A drone is conducting a search pattern over a rectangular field. The drone's current position relative to its control station is at Cartesian coordinates (-4, 4√3) meters. The search coordinator needs to convert this position to polar coordinates to program the drone's next movement. What are the polar coordinates (r, θ) of the drone's position, with r measured in meters and θ measured in radians between 0 and 2π?

…and 5 more problems

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. A marine biologist is tracking a dolphin's position using an underwater coordinate system. The dolphin is currently located at rectangular coordinates (-3, -3√3) meters from the research station. To program an autonomous underwater vehicle to intercept the dolphin, the biologist needs to convert these coordinates to polar form (r, θ) where r > 0 and θ is measured in radians between 0 and 2π. What polar coordinates should the biologist use?
3. Convert the rectangular coordinates (-7, 7√3) to polar form (r, θ) where r > 0 and 0 ≤ θ < 2π.

…and 5 more problems