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December 21, 2014

December 21, 2014

Posted by **v** on Tuesday, November 13, 2012 at 11:54pm.

- trigonometry -
**v**, Tuesday, November 13, 2012 at 11:59pmactually could i take the arctan of -5/4? would that give me the degree?

- trigonometry -
**Reiny**, Wednesday, November 14, 2012 at 9:40amarctan (-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

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