Modifying The Angle of a Unit Vector

I have an angle in the form of a unit vector. I need to be able to change this angle. Say the angle of the vector V = (x,y) is currently A. How would I go 开发者_Python百科about changing the angle to A+0.2 (that is just an example, it could be any value I'm adding) without converting the vector to an angle, modifying it, then calculating the appropriate vector again?

---

Using the following formulae to rotate your vector counter-clockwise:

therefore to rotate the vector V = (x, y) pi an angle A you would do the following:

V' = (x * cos(A) - y * sin(A), x * sin(A) + y * cos(A))

or with code:

vec2 rotateVec2(const vec2 &vec, float angle)
{
    float newX = vec.x * cos(angle) - vec.y * sin(angle);
    float newY = vec.y * sin(angle) + vec.y * cos(angle);
    return vec2(newX, newY);
}

---

x2 = x * cos(angle) - y * sin(angle);
y2 = y * cos(angle) + x * sin(angle);