Distance Between Any Two Points on a Unit Circle

$\begingroup$

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

$\endgroup$ 4

2 Answers

$\begingroup$

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

$\endgroup$ 4 $\begingroup$

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.

$\endgroup$ 0

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy