Expert: Paul Klarreich - 10/29/2008

Question
Lets say I have an angle that is -3 rads. Is there a supplement to it? I answered this question on a quiz and got it wrong for saying the answer is approx. - 0.14 rads. My pre-calc teacher says there is no supplement because you can't have negative distance. I think that my answer is right because it isn't negative distance. The negative sign doesn't mean negative distance; it means in a clockwise direction:

-3 rads = 3 rads in a clockwise direction

Am I right? My teacher also told me that there is no such thing as negative velocity because you can't have a negative distance but I tried to tell her you could. Negative velocity is velocity in the opposite direction. Hopefully someone can clear this up.

Answer
Questioner:   Tyler Beyett
Category:  Advanced Math
Private:  No
 
Subject:  Supplementary Angle in Radians Question
Question:  Lets say I have an angle that is -3 rads. Is there a supplement to it? I answered this question on a quiz and got it wrong for saying the answer is approx. - 0.14 rads. My pre-calc teacher says there is no supplement because you can't have negative distance. I think that my answer is right because it isn't negative distance. The negative sign doesn't mean negative distance; it means in a clockwise direction:

-3 rads = 3 rads in a clockwise direction

Am I right? My teacher also told me that there is no such thing as negative velocity because you can't have a negative distance but I tried to tell her you could. Negative velocity is velocity in the opposite direction. Hopefully someone can clear this up.
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Hi, Tyler,

Of course there is a supplement, and it contains no steroids, either. (Sorry - I couldn't resist.)

If  x is any angle, pi - x  is its supplement.  (I assume you are using radians, as you said -- degrees are for children.)

So if  x = -3,  pi - (-3) or  pi + 3 is definitely its supplement.  Supplementary angles ALWAYS ALWAYS ALWAYS add up to pi, and  -3 + (pi + 3) = pi.

Your teacher is not correct -- you can have a supplement that is a negative angle.  However, your answer was wrong, too.  

I think you simply blew a sign to get your -0.14.  You did  pi - 3 instead of pi - (-3).

You are correct, also, that there is such a thing as negative velocity. (Not speed, mind you.) Check out:

http://ocw.mit.edu/OcwWeb/Physics/8-01Physics-IFall1999/VideoLectures/detail/emb...

It's a long download, but worth it.

And don't give up -- the calculus teachers are much better.