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Showing posts from July, 2013

### Special Relativity and Hyperbolic Trigonometric Functions

Just a few brief notes on circular and hyperbolic trigonometry today.  First, if there's anyone who'd like to offer, any clarifications, expansions, or other cool and interesting facts, please, you're more than welcome!  As usual, this is stuff that I learned in high school that didn't become blindingly clear and meaningful until it cropped up in grad school physics.  First, the equations for the circle and the hyperbola (picture 1)

Notice that they differ only by a single negative sign.  Now, for their graphs, (picture 2).

Each of these figures can also be expressed in parametric form as follows, (this is where the trigonometric and hyperbolic trig functions come in).  (picture 3)

Now for the notes and other thoughts.

Angular Arc Length and Angular Area
Until just a few weeks ago, I had always wondered why the inverse trig functions were called arcsine, and arccosine.  The answer makes perfect sense, it just hadn't occurred to me.  The arc prefix indicates that the…