How to calculate the polar angle from Cartesian coordinates?

To calculate the polar angle from Cartesian coordinates, use the formula θ = arctan(y/x).

When given a point in Cartesian coordinates (x,y), the polar angle θ can be found using the formula θ = arctan(y/x). This formula calculates the angle between the positive x-axis and the line connecting the origin to the point (x,y). It's useful to understand trigonometric ratios which underpin this calculation.

It is important to note that the arctan function returns an angle in radians, so the answer should be converted to degrees if necessary. This can be done by multiplying the answer by 180/π. If you're working with trigonometric identities, see more on how these are applied in Trigonometric Identities.

For example, if given the point (3,4), the polar angle can be found as follows:

θ = arctan(4/3)
θ ≈ 0.93 radians
θ ≈ 53.13 degrees

A-Level Maths Tutor Summary: To find the polar angle θ from Cartesian coordinates (x,y), apply the formula θ = arctan(y/x). Remember, this gives θ in radians. To convert to degrees, multiply by 180/π. For example, point (3,4) has a polar angle of roughly 0.93 radians or 53.13 degrees. This method helps us understand the angle's direction in a plane. For further reading on calculating angles, explore the Inverse Trigonometric Functions.