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