$SPAD/src/input sincosex.input

Timothy Daly December 3, 2016

Abstract

Contents

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1 License

— license —

--Copyright The Numerical Algorithms Group Limited 1991.

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— * —

)set break resume
)spool sincosex.output
)set message test on
)set message auto off
)clear all
--S 1 of 1
sinCosExpand := rule
  sin(-x)    == - sin(x)
  cos(-x)    == cos(x)
  sin(x + y) == sin(x) * cos(y) + sin(y) * cos(x)
  cos(x + y) == cos(x) * cos(y) - sin(x) * sin(y)
  sin((n | integer? n and n > 1) * x) ==_
       sin(x) * cos((n-1)*x) + sin((n-1)*x) * cos(x)
  cos((n | integer? n and n > 1) * x) ==_
       cos(x) * cos((n-1)*x) - sin(x) * sin((n-1)*x)
--R
--R
--R   (1)
--R   {- %B sin(x) == - %B sin(x), cos(x) == cos(x),
--R    sin(y + x) == cos(x)sin(y) + cos(y)sin(x),
--R    cos(y + x) == - sin(x)sin(y) + cos(x)cos(y),
--R    sin(n x) == cos(x)sin((n - 1)x) + cos((n - 1)x)sin(x),
--R    cos(n x) == - sin(x)sin((n - 1)x) + cos(x)cos((n - 1)x)}
--R                           Type: Ruleset(Integer,Integer,Expression(Integer))
--E 1
)spool
)lisp (bye)

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References^{[1] nothing}

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