Convert the Cartesian coordinates to polar coordinates.

Question: Convert the Cartesian coordinates to polar coordinates.

Answer: To convert Cartesian coordinates (x,y) to polar coordinates (r,θ), use the formulas r = √(x² + y²) and θ = tan⁻¹(y/x).

To convert Cartesian coordinates to polar coordinates, we need to find the distance from the origin to the point (x,y) and the angle that the line connecting the origin and the point makes with the positive x-axis.

The distance from the origin to the point (x,y) is given by the formula r = √(x² + y²). This is the length of the hypotenuse of the right-angled triangle formed by the x and y coordinates.

The angle that the line connecting the origin and the point makes with the positive x-axis is given by the formula θ = tan⁻¹(y/x). This is the angle between the line and the x-axis, measured in a counterclockwise direction.

For example, let's convert the Cartesian coordinates (3,4) to polar coordinates. Using the formulas above, we have:

r = √(3² + 4²) = √25 = 5
θ = tan⁻¹(4/3) ≈ 0.93 radians

Therefore, the polar coordinates of the point (3,4) are (5,0.93).