Trig review

Etymology:
- draw picture w/ inner, outer triangles
  it's all -ratios-
  to simplify, make radius 1
  now sine, tan, sec (and cosine) are all the lines;
  draw complimentary triangles to say "ditto for co-stuff"
  
  sin2 + cos2 = 1
  tan2 + 1 = sec2
  ...are now obvious
  (and they're the same formula, up to rescaling,
   which is obvious from the picture!)
  
  tan = touch
  sec = cut (bi-sect, dis-sect)
  sine -- long story (ad-jira -> lose consonants in arabic, think it's
  "bay", so becomes "sinus")
  co = complimentary, duh

- interpretation
  sine is area (of parallelogram)
  cosine is -projection-
  tan is slope
  (and thus arcsine, arccosine, arctan recover angle from
   area/projection/slope;
   in linear algebra can kinda use arccosine,
   and arctan is the most generally useful)

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NB: I never use these formulae on a regular basis

- angle addition :: interesting,
  easy to see with linear transforms
  (equiv., from complex exponentials and demoivre's thm)

- (half-angle: prolly can do from linear algebra)

- product->sum/sum->product: hetrodyne!
  (beat frequencies)
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NB: make de moivre's theorem the -centerpiece- of 3rd quarter.
