SOLUTION: To whom it may concern, what is the relationship between cotangent theta and cotangent NEGATIVE theta? Can you please give me 7 or 10 examples to work with. I really need to learn

Question 689854: To whom it may concern,
what is the relationship between cotangent theta and cotangent NEGATIVE theta? Can you please give me 7 or 10 examples to work with. I really need to learn this immediately for an upcoming exam. Please reply ASAP. A thousand thank yous won't be enough.
-Lex

Found 2 solutions by KMST, lwsshak3:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
because
,
and,
as and , then

Angles measuring (AOB), (AOC), (AOD), ... are represented.

For the or angle AOB:
, and are the x and y coordinates of point B

The reflection of angle AOB is the or angle AOB':
, , and

For the angle AOC and its reflection, the angle AOC':
, ,
, and , so

For the angle AOD and its reflection, the angle AOD':
, ,
, and , so
and

For the angle AOE and its reflection, the angle AOE':
, ,
, and , so

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
what is the relationship between cotangent theta and cotangent NEGATIVE theta?
cot(x)=-cot(-x) (this is called an odd function, compared to an even function)
Examples:
pick angle of 45� in quadrant I
this gives you a reference angle of 45� where cot 45�=1
-45� will also give you a reference angle of 45� but in quadrant IV where cot -45=-1
..
pick angle 135� in quadrant II
this gives you a reference angle of 45� where cot135�=-1
-135� will also give you a reference angle of 45� but in quadrant III where cot-135�=1
..
pick angle 225� in quadrant III
this gives you a reference angle of 45� where cot225�=1
-225� will also give you a reference angle of 45� but in quadrant II where cot-225�=-1
..
note: I used a reference angle of 45� for the examples but this will hold true for any reference angle.
This will also hold true for the tan function since cot is the reciprocal of tan.
A negative angle means rotating in a clockwise direction and a positive angle in a counter-clockwise direction.The value for the trig functions and their reciprocals is computed from the reference angle and the sign depends on which of the 4 quadrants the angle is in. See if you can apply this method to the sin and cos functions.
..
Hope this helps!
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