How to calculate the angle in polar coordinates?

To calculate the angle in polar coordinates, use the formula θ = tan⁻¹(y/x).

In polar coordinates, a point is represented by its distance from the origin (r) and the angle it makes with the positive x-axis (θ). To find the angle θ, we use the formula θ = tan⁻¹(y/x), where y is the vertical distance from the origin and x is the horizontal distance from the origin.

For example, consider the point (3, 4) in polar coordinates. To find the angle θ, we first need to find the values of x and y. In this case, x = 3 and y = 4. We can then use the formula θ = tan⁻¹(y/x) to find the angle:

θ = tan⁻¹(4/3)
θ ≈ 0.93 radians

Therefore, the angle θ for the point (3, 4) in polar coordinates is approximately 0.93 radians.

It is important to note that the angle θ can also be expressed in degrees by converting radians to degrees using the formula θ (in degrees) = θ (in radians) × 180/π. In the example above, the angle θ in degrees would be approximately 53.13°.