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As part of a larger investigation, I am required to be able to calculate the distance between any two points on a unit circle. I have tried to use cosine law but I can't determine any specific manner in which I can calculate theta if the angle between the two points and the positive axis is always given.

Is there any manner in which I can do this?

Thanks

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    Yes I did...I'll try to look i$n$to that.2012-04-21

2 Answers 2

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If the arc distance between the two points is $\theta$, the length of the chord between them is $2\sin\frac{\theta}{2}$:

geometry diagram

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    That diagram rates a +1! :-)2012-04-21
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Hint

  • Points on the unit circle centered at $(0,0)$ on the argand plane are of the form $(\cos \theta, \sin \theta)$, with $0 \leq \theta \lt 2\pi$.

  • Can you use distance formula now to calculate the requires to distance?


With some knowledge in complex numbers, you'd realise that, if $z_1$ and $z_2$ are two complex numbers, the amplitude, $|z_1-z_2|$ is the distance between the two of them.