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August 29, 2014

August 29, 2014

Posted by **Mayhem** on Saturday, February 25, 2012 at 2:46am.

- Precal -
**Reiny**, Saturday, February 25, 2012 at 9:59amyou are correct to say that by adding 2π , one rotation , we point ourselves in the same direction,

how about 4π ? , or 6π or n(2π) where n is whole number?

so now the 2nd of their answer should make sense they have simply added multiples of 2π to get

(-1, -2π/3) = (-1, -2π/3 +2nπ)

now look at their 1st answer.

Did you notice that the -1 changed to +1 ?

That would have been a reversal of direction of 180° or π

let n = 0

we get (-1, -2π/3) ---> (+1, 2π/3 + π) or (1, 5π/3)

let's look at this in degrees .....

(-1, -120°) ---> (1, 120 + 180) = (1,300)

At this point we should realize that their 1st answer cannot be correct, since we don't end up at the same endpoint.

(-1, -120°) means: point yourself in the direction of -120

but then go -1 unit, or go 1 unit in the OPPOSITE direction, so the simplest version of

(-1,-120°) = (1,60°) or (1, π/3)

To show it is wrong .....

There has to be an integer value of n such that

2π/3 + (2n+1)π = π/3

2/3 + 2n+1 = 1/3

2n = 4/3

n = 2/3, but n has to be an integer.

so they are wrong.

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