Does the angle between the x axis and a vector have to be counterclockwise?

Question

I was solving problems and found out that the answers were mearsured counterclockwise even if it over pi (180 degrees). Is it available to measure the angle between the vector and the +x vector (1,0) or is it formally defined as counterclockwise? if so, in which field are those defined?

Thank you!:)

Answer 1

Yes, mathematicians nearly always measure angle anticlockwise, even when that angle is more than 180 degrees.

In certain physical applications, however, such as aerial and ocean navigation, it is very common to specify a direction relative to a fixed reference vector, such as magnetic north, giving both the angle and the direction of rotation.

Answer 2

It seems the trigonometric functions are defined based on a counter-clockwise angle with the x-axis. If it were a clockwise angle we would have things like $sin (\frac\pi4)=-\frac {\sqrt{2}} 2$. So in short it would change everything around... Hence we have to follow the convention. ..