What is the orientation of: p = (3, -4)T ?
Answer:
Plugging the numbers into the MS Windows calculator:
arc tan( y/x ) = arc tan( -4/3 ) = arc tan( -1.333333333333 ) = -53.13°
What is the orientation of: p = (3, -4)T ?
Plugging the numbers into the MS Windows calculator:
arc tan( y/x ) = arc tan( -4/3 ) = arc tan( -1.333333333333 ) = -53.13°
The calculation looks about right, in the diagram. If you want the angle to be expressed as a counter-clockwise rotation, then it is 360° - 53.130° = 306.870°
Sadly, it looks like the vector -p will give you the same result. So what to do? Always sketch the vector when you are computing its orientation. Then you can see that the angle you want for -p is 180° - 53.130° = 126.87° .
In most programming languages, the function atan2(y, x) is available.
It computes the angle in radians between the positive x-axis and the point given by the coordinates (x, y).
It uses the signs of x and y to determine the correct quadrant for the angle.
What is the orientation of u = (-4, -2)T ? (Sketch the vector first, then use a calculator.)