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Trig functions

  1. Jan 8, 2005 #1
    I believe that calculators use Taylor expansions to compute sines, cosines and tan's based upon the argument [itex]\theta[/itex] (in radians of course). However, my question is, aside from these expansions, is there some sort of link between [itex]\theta[/itex] and the output of the function itself.

    I mean I know that [itex] \cos{\theta} = \frac {adj}{hyp}[/itex] and the other trig ratios, but was this just worked out by hand, pencil and paper and kept in a tabular form before the Taylor expansion was devised? Is there a direct link between [itex] (\frac{adj}{hyp}) [/itex] and [itex]\theta[/itex].

    Get me?!
  2. jcsd
  3. Jan 8, 2005 #2


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    Trig values were, yes, worked out by hand (:yuck:)

    One of Ptolemy's major contributions to Greek maths was his trig tables.
    The Indian mathematicians did the same, but independently of the Greeks.

    Hmm..now that I reread your question, it seems you were after something else..
  4. Jan 8, 2005 #3
    No thats a great answer.. just curious. I know the Maclaurin series for trig functions takes the parameter and manipulates it to get a solution. However I wanted to know if there was some other relation between the argument and the answer. Say I had the angle [itex]\frac{\pi}{9}[/itex] and I wanted to know the cosine of it, that is the ratio of the adjacent to the hypotenuse, then was there some algebraic manipulation you could do with the value [itex]\frac{\pi}{9}[/itex] to yield the solution.

    Aside from doing it by hand, I was curious whether it could be done another way before the days of calculus.
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