Quick Vector question - finding the angle of inclination (1 Viewer)

[tk8]

Find the angle of inclination of this vector :

My answer was π/6 , but apparently, it is supposed to be 5π/6 . It'd be great if someone could explain why

 

[ExtremelyBoredUser]

Find the angle of inclination of this vector :View attachment 35476

My answer was π/6 , but apparently, it is supposed to be 5π/6 . It'd be great if someone could explain why

You got pi/6 since you calculated the inside angle from doing tan^-1(y/x) but you didn't consider the region it is in. Its in the 2nd region so it is pi/6 above the negative x axis or 5 pi/6 from the positive axis. You would just do pi - pi/6 to find the angle of inclination in this case. So you would say formally it has an angle of 5pi/6.

 

[tk8]

You got pi/6 since you calculated the inside angle from doing tan^-1(y/x) but you didn't consider the region it is in. Its in the 2nd region so it is pi/6 above the negative x axis or 5 pi/6 from the positive axis. You would just do pi - pi/6 to find the angle of inclination in this case. So you would say formally it has an angle of 5pi/6.

View attachment 35477

Thanks! Does the angle of inclination always have to be from the positive axis?

 

[mmmmmmmmaaaaaaa]

When doing these question all you need to know is what quadrant it is in and the tan^-1(y/x)
ie.
first quadrant - tan^-1(y/x)
second quadrant - pi - tan^-1(y/x)
third quadrant - pi + tan^-1(y/x)
fourth quadrant - 2pi - tan^-1(y/x)