## Hyperbola Trig

(Lecture: 15 minutes)

• Define hyperbolic trig functions as coordinates on unit hyperbola.
• “Angle” is (Lorentzian) arclength.
• Recover usual definitions (via hard integrals).
• Relate to constancy of speed of light.

Based on §4 of the text, especially §4.1 and §4.2.

### Reflections

Having just reviewed circle trigonometry (in this lecture), this lecture repeats this familiar derivation in an unfamiliar context. But only the details are different, at least algebraically. Geometrically, the fundamental difference is that hyperbolas have two branches, separated by distinguished asymptotes at 45 degrees. Remind students that the speed of light is supposed to be special, and that slopes are speeds!

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