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Math Help - trig

  1. #1
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    trig

    can anyone tell me a method of finding sin and cos of arbitrary angles like 53 , 57 AND 63 DEGREE
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  2. #2
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    Quote Originally Posted by abhishek arora View Post
    can anyone tell me a method of finding sin and cos of arbitrary angles like 53 , 57 AND 63 DEGREE
    Use the Taylor series expansions.

    \sin{x} = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \frac{x^9}{9!} - \frac{x^{11}}{11!} +\dots

    \cos{x} = 1  - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \frac{x^8}{8!} - \frac{x^{10}}{10!} + \dots


    The further you go along the series, the more accurate your answer will be.
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  3. #3
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    Quote Originally Posted by Prove It View Post
    Use the Taylor series expansions.

    \sin{x} = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \frac{x^9}{9!} - \frac{x^{11}}{11!} +\dots

    \cos{x} = 1  - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \frac{x^8}{8!} - \frac{x^{10}}{10!} + \dots


    The further you go along the series, the more accurate your answer will be.
    I should add a warning that the Taylor series expansions are for angles in radians not degrees so you'd have to convert your angles first.

    As a quick reference 1 degree = \frac{\pi}{180}radians
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  4. #4
    Senior Member pacman's Avatar
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    i stumbled upon this exact trigonometric values, very good!

    Exact trigonometric constants - Wikipedia, the free encyclopedia

    [edit] 3: 60-sided polygon
    [edit] 6: 30-sided polygon

    [edit] 9: 20-sided polygon

    [edit] 12: 15-sided polygon

    [edit] 15: dodecagon

    [edit] 18: decagon

    [edit] 21: sum 9 + 12

    [edit] 22.5: octagon

    [edit] 24: sum 12 + 12

    [edit] 27: sum 12 + 15

    [edit] 30: hexagon

    [edit] 33: sum 15 + 18

    [edit] 36: pentagon

    [edit] 39: sum 18 + 21

    [edit] 42: sum 21 + 21

    [edit] 45: square

    [edit] 60: triangle

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  5. #5
    Senior Member pacman's Avatar
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    Sin[57] = Cos[33] ≈ 0.838670567945 =

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