0
$\begingroup$

I'm trying to find the angle subtended by the unit hyperbola through the point (1,0). I think that I should be integrating something, but I'm not sure how to set it up. I've been trying to think of this as it would be related to a unit circle, where we would have $R=1$ and then the following $$ \int_0^{\theta_{0}} R^2(\sin^2\theta+\cos^2\theta)d\theta=R^2\int_0^{2\pi}d\theta=(1)(2\pi)=2\pi $$ So the angle subtended would just be $2\pi$. I know that $1=\cosh^2 x-\sinh^2 x,$ but as I'm only interested in the right hyperbola, I'm not sure I can use the same trick. Beyond this, I'm stuck. Any ideas? Thank you!

$\endgroup$

1 Answer 1

0
$\begingroup$

Read $\;$G.A.Jennings Modern Geometry with Applications (1994) pp.178-179.

There you find a definition of hyperbolic angle (p.178) and a formula (p.179).

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .