Laguerre cosine approximation<*** End of File ***>
Math history fun fact
I came across this some 50 years ago,
before calculators had trig keys.It's good to about 4 significant digits for first quadrant,
and exact at 0, 45, 60, 90 degrees.m = angle/90 for degrees or angle/pi/2 for radians
-m^2
( --------------------------------- - 1)
sqrt((-m^3 + 4m^2 -5m + 2)/3) + mThis can be expressed in linear form as:
-(((((((4-m)m-5)m+2)/3)^(1/2)+m)^(-1)mm)-1)
which can be keyed in directly on a simple chain-logic memory
calculator with a square root key and the ability to find the
reciprocal using some combination of / and = keys. Handle the
leading minus at the end, just mentally if necessary.To test it, on a 12C, for angles in degrees:
90 / ENTER ENTER ENTER
4 x<>y - X 5 - X 2 + 3 / g-sqrt + 1/x X X 1 - CHS
OT: Cosine curio
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