If you’re given the components of a vector, such as (3, 4), you can convert it easily to the magnitude/angle way of expressing vectors using trigonometry.

For example, take a look at the vector in the image.

Suppose that you’re given the coordinates of the end of the vector and want to find its magnitude, v, and angle, theta. Because of your knowledge of trigonometry, you know

y/x = v sinθ/ v cosθ = tanθ

Where tan theta is the tangent of the angle. This means that

theta = tan^–1(y/x)

Suppose that the coordinates of the vector are (3, 4). You can find the angle theta as the tan^–1(4/3) = 53 degrees.

You can use the Pythagorean theorem to find the hypotenuse — the magnitude, v— of the triangle formed by x, y, and v:

v = √ x² + x²

Plug in the numbers for this example to get

v = √ 3² + 4²

So if you have a vector given by the coordinates (3, 4), its magnitude is 5, and its angle is 53 degrees.