How to rotate a vector without error?

Question

JavaScript

There are the following elements:
Vector Coordinate rotation function
a = {x: 1, y: 0}

function rotate(angle) {
  a.x = a.x * Math.cos(angle) - a.y * Math.sin(angle);
  a.y = a.x * Math.sin(angle) + a.y * Math.cos(angle);
}

Which is called in this way The problem is that with each turn, accuracy is lost. This can be detected by checking the length of the vector. Initially, the length is 1 after 10 calls - 0.9999671067997294 after 100 - 0.9831222411821932 And so on. Moreover, if you increase the rotation angle when calling rotate, then the error increases. Please tell me what is the reason and how to get rid of this error? Maybe it's worth using another way to rotate the coordinates? Which?
rotate(1 * Math.PI / 180);
Math.sqrt( Math.pow(a.x, 2) + Math.pow(a.y, 2) )

Answer 1

To maintain accuracy, you will have to store the entire history of rotations with the preservation of the sign (clockwise +, counterclockwise -) and to calculate the latter - sum the degrees.