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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!:)

Orangecal
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  • In navigation, the orientation of angles is typically clockwise. In math, the usual convention is counterclockwise. We pick one orientation or the other and stick to it within a field of study. If you didn't have a convention to measure the angle using the same orientation every time, how would you get angles greater than 180 degrees? – David K Jul 31 '17 at 01:00

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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.

Michael Cromer
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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. ..