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# Do we use negative angles? watch

1. Howdy . When do we use negative angles?

I am just reading that an angle can be negative is measured, on a co-ordinate system, clockwise.

Why would we use the negative angle in some real world examples?

Thanks
2. (Original post by marcus888)
Howdy . When do we use negative angles?

I am just reading that an angle can be negative is measured, on a co-ordinate system, clockwise.

Why would we use the negative angle in some real world examples?

Thanks
In the Cartesian world it doesn't matter if the angle is positive or negative. In the world of polar co-ordinates it does because r = - theta doesn't make sense (r >= 0)
3. (Original post by marcus888)
Howdy . When do we use negative angles?

I am just reading that an angle can be negative is measured, on a co-ordinate system, clockwise.

Why would we use the negative angle in some real world examples?

Thanks
This pops up when dealing with the complex plane all the time especially when specifying complex numbers in the form and this is used in engineering I believe but I don't know the specifics.
4. (Original post by marcus888)
Howdy . When do we use negative angles?

I am just reading that an angle can be negative is measured, on a co-ordinate system, clockwise.

Why would we use the negative angle in some real world examples?

Thanks
Also in pure Euclidean geometry, there's a notion of directed angles which can be useful in doing proofs where the given data could imply two different configurations, and you don't want to do a separate proof for each case. See http://www.mit.edu/~evanchen/handout...ted-Angles.pdf
5. (Original post by marcus888)
Howdy . When do we use negative angles?

I am just reading that an angle can be negative is measured, on a co-ordinate system, clockwise.

Why would we use the negative angle in some real world examples?
Two big reasons:

(1) Convenience: it reduces the number of different cases we need to think about. There was a time when we didn't allow negative numbers in polynomials, and it meant that there wasn't one quadratic formula, but a whole set of them (with different methods for ax^2+bx+c = 0, ax^2+bx = c, ax^2 + c= bx, etc). We don't want to go back to those dark times...

(2) Behaviour near 0º with small changes. If our angle A is 1º, and we don't allow negative angles, there's no "good" solution to what A - 2º is. We can say it's 359º (wrapping round), but then we have a big change in angle which doesn't feel right. Or we can say it's 1º (but in the other direction), but how do we keep track of the direction and distinguish between that and the original angle A.

The latter is very much the show stopper, but the first reason would be enough to justify negative angles all by itself IMHO.
6. Negative angles are useful in electronics to show when two sinusoidal wave forms (e.g. current and voltage) are out-of-phase. We can describe the "lag" using a negative angle.

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