SOLUTION: What is the difference between a positive and a negative angle?

Question 950279: What is the difference between a positive and a negative angle?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
it has to do with the direction of rotation in the unit circle.
the positive angle rotates in a counter-clockwise direction.
the negative angle rotates in a clockwise direction.
that's all that i know about it.
i'm sure there are real world applications of negative and positive angles, but i'm not familiar with them.
i only know the difference form the perspective of the unit circle and finding the trig function of the angle.
when you're analyzing the trig functions of the angle, it's helpful to convert the negative angle to it's equivalent positive angle between 0 and 360 degrees and then to find the reference angle.
for example:
an angle of -800 degrees can be turned into an equivalent positive angle by dividing it by 360 and then rounding up and then adding that number times 360 to it in order to get the positive angle between 0 and 360 degrees.
-800 / 360 = 2 plus a remainder.
add 3 * 360 to it to get -800 + 1080 = 280
that's a positive angle between 0 and 360 degrees.
it's in the fourth quadrant because it's between 270 and 360 degrees.
the reference angle is therefore 360 - 280 = 80 degrees.
you can find it's trig functions using a calculator.
the only difference between the angle in the first quadrant and the fourth quadrant is the sign of the trig function.
in the first quadrant all trig functions are positive.
in the fourth quadrant, sine is negative, cosine is positive, tangent is negative. the reciprocal functions carry the sign of their reciprocals.
cosecant takes sign of sine. secant take sign of cosine. cotangent takes sign of tangent.
for example:
sine of 80 is equal to .9848...
sine of 280 is equal to -.9848...
sine of -800 is equal to -.9848...
same trig function but different sign if it's in the fourth quadrant as opposed to if it's in the first quadrant.
your scientific calculator will usually find the trig function for you directly, i.e. put in sin(-800) and you'll get -.9848...
where the calculator falls down is when you give it a sine of -.9848... and want it to find the angle.
it will then give you the smallest angle it can find that has that trig function.
arc-sine of -.984807753 is equal to -80 degrees.
that's correct, but maybe not the angle you are looking for.
to convert that to an equivalent positive angle, just add 360 to it and you will get 280 degrees.
find the reference angle for 280 degrees and you will get 80 degrees.
that's the equivalent angle in the first quadrant.
in electronics, you can have negative and positive phase shifts.
these would be represented by negative and positive differences in angles.
i'm sure there are others.
i just don't know them.
you can try a google search on practical applications of negative an dpositive angles.
something might pop up.
perhaps in engineering and ehcmistry.
possibly in astronomy.

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