Question

Convert from cylindrical coordinates to cartesian coordinates

Answer 1

To convert from cylindrical to Cartesian coordinates, use the equations x = r × cos(θ) and y = r × sin(θ), where r is the radial distance to the origin and θ is the angle with the positive x-axis. For example, a point with polar coordinates (47/3, 5.50 m) converts to Cartesian coordinates approximately (15.45 m, -1.31 m).

Step-by-step explanation:

To convert from cylindrical coordinates to Cartesian coordinates, a point in the plane can be described using either a Cartesian coordinate system (x, y) or a polar coordinate system (r, θ). The conversion between these two systems is given by the equations:

• x = r × cos(θ)

• y = r × sin(θ)

Where r is the radial coordinate, representing the distance from the origin to the point, and θ (theta) is the angle formed between the line from the origin to the point and the positive x-axis.

For example, if the polar coordinates of a point are (47/3, 5.50 m), the Cartesian coordinates (x, y) can be calculated as follows:

• x = (47/3) × cos(5.50) = 15.45 m (approximately)

• y = (47/3) × sin(5.50) = -1.31 m (approximately)

These values represent the position of the point in a coordinate system with the origin at the center of the plane.