A basic trigonometry question

Discussion in 'General Math' started by gerard46, Feb 8, 2004.

  1. gerard46

    gerard46 Guest

    | Walt L. Williams wrote:
    | I am a student enrolled in a
    | trigonometry course. I tend to be
    | curious sort.
    |
    | My textbook has an example in it:
    |
    | sin34(deg symbol) 30(minute symbol)
    | (My usenet client doesn't have the
    | little degree and minute symbols.)
    | It gives the answer of .566406237
    |
    | The fact that I am able to put in
    | only a degree amount and get back
    | a figure indicates that "sin" has
    | a value associated with it. (The
    | same would most likely be true for
    | "cos" & "tan".) What is that value?
    | Is there a web site out there that
    | would have this information?
    |
    | The text book seems to be quick to
    | get one to punch into a calculator.
    |
    | I want to know how it actually works.

    There are 60 minutes to a degree,
    and also 60 seconds to a minute.

    So 30 degrees and 30 minutes is
    equivalent to 30.5 degrees. _____________Gerard S.
     
    gerard46, Feb 8, 2004
    #1
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  2. Greetings

    I am a student enrolled in a
    trigonometry course. I tend to be
    curious sort.

    My textbook has an example in it:

    sin34(deg symbol) 30(minute symbol)
    (My usenet client doesn't have the
    little degree and minute symbols.)
    It gives the answer of .566406237

    The fact that I am able to put in
    only a degree amount and get back
    a figure indicates that "sin" has
    a value associated with it. (The
    same would most likely be true for
    "cos" & "tan".) What is that value?
    Is there a web site out there that
    would have this information?

    The text book seems to be quick to
    get one to punch into a calculator.

    I want to know how it actually works.
     
    Walt L. Williams, Feb 8, 2004
    #2
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  3. gerard46

    David Moran Guest

    I'd do a search for power series, these are what your calculator probably
    uses. You probably won't see power series until calculus.

    David Moran
     
    David Moran, Feb 8, 2004
    #3
  4. For a trigonometry course, you probably want to define the sine of an angle
    as follows. If you draw a right triangle with an acute angle alpha (angles
    traditionally get Greek letters, even though you can't print them in
    127-character ASCII), then the sine of alpha, written sin(alpha), is the
    side opposite alpha divided by the hypotenuse. Similarly, cosine is
    adjacent side divided by hypotenuse, and tangent is opposite over adjacent.

    This should be in your textbook.

    Now, the problem is, that this is a really bad way to calculate the trig
    functions. First of all, measurement errors (with real triangles) creep in
    and make it really hard to get good values. But secondly, measuring is
    really a lousy way to calculate.

    So starting about 2300 years ago, mathematicians (actually, originally,
    astronomers) calculated tables of sines and cosines and tangents, so that
    they just had to look them up instead of calculating them. But to calculate
    the tables, they still didn't want to measure.

    There are some special angles that we know the values of the trig functions.
    for example, sin(30 degrees) = 1/2 (exactly). We can then calculate some
    other angles using the half-angle formulas, and then build up a table using
    angle addition formulas. It's a lot of work, and then, when you want to use
    the functions, you have to look them up in a table and copy them down. This
    introduces another chance for error.

    So when computers appeared, calculating trig functions was a fairly high
    priority. When they became small enough to hold in your hand, calculating
    trig functions was a godsend. You just punch the numbers and out pops the
    answer, without copying numbers down and making errors and checking and all
    that stuff. (And it's always right because you never punch the wrong key,
    and everyone who uses a calculator understands what they're doing and so
    always use the correct formulas.)

    The most widespread method of calculating trig functions is the CORDIC
    algorithm. I don't know if there are other widespread methods of if it's
    the only widespread one.

    Jon Miller
     
    Jonathan Miller, Feb 10, 2004
    #4
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