- #1
snoopies622
- 840
- 28
I know if we set
[tex] x = \cosh \theta , y = \sinh \theta [/tex]
and graph for all [itex] \theta [/itex]'s, we get a hyperbolic curve since then
[tex]
x^2 - y^2 = 1.
[/tex]
But — unlike the case of making a circle by setting
[tex] x = \cos \theta , y = \sin \theta [/tex]
and graphing all the [itex] \theta [/itex]'s — in the hyperbolic graph the angle formed by the line connecting a point (x,y) to the origin and the positive x-axis is not the corresponding angle [itex] \theta [/itex], making the original designations
[tex] x = \cosh \theta , y = \sinh \theta [/tex]
seem rather arbitrary, no?
[tex] x = \cosh \theta , y = \sinh \theta [/tex]
and graph for all [itex] \theta [/itex]'s, we get a hyperbolic curve since then
[tex]
x^2 - y^2 = 1.
[/tex]
But — unlike the case of making a circle by setting
[tex] x = \cos \theta , y = \sin \theta [/tex]
and graphing all the [itex] \theta [/itex]'s — in the hyperbolic graph the angle formed by the line connecting a point (x,y) to the origin and the positive x-axis is not the corresponding angle [itex] \theta [/itex], making the original designations
[tex] x = \cosh \theta , y = \sinh \theta [/tex]
seem rather arbitrary, no?