Posted by v on Tuesday, November 13, 2012 at 11:54pm.
actually could i take the arctan of -5/4? would that give me the degree?
arctan (-5/4) = appr -51.34°
which would be a "clockwise" rotation and place you in quadrant IV
and stating it as a positive rotation would be 308.66°
In this case you answer is correct, but we lucked into it
Let me explain:
suppose your point had been (-4,5) which would be an angle in the second quadrant.
Your calculations of arctan (5/-4) would give us the same -51.34° , but it would not be correct.
Calculators have been programmed to give the closest angle to zero when doing any arc(trigfunction)
Since there are two answers for any arc(trigfunction) , the calculator cannot know which angle you want, and you have to establish that yourself using the good ol' CAST rule.
What I do is to use the positive fraction in my arctan, knowing from the point where the angle is
e.g. what angle does the terminal arm ending at (-4,5) make with the x-axis?
arctan (+4/5) = 51.34°
but I know I am in quadrant II, so the actual angle is
180-51.34 or 128.66°
In general, after you find the angle Ø in standard position (quad I ),
for
Quadrant I : your angle is Ø
Quadrant II : your angle is 180-Ø
Quadrant III: your angle is 180+Ø
Quadrant IV : your angle is 360-Ø