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Math help

Mr. Cucumber
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Suppose I have to calculate sinX where can X is 43 degrees... My calculator says 0.68199836 ...but how is that calculated... I know there are bunch of videos and articles telling how to calculate from reference angles. .but no .. I want to know how it is actually... Like how does my calculator calculate that sine 43 is that specific value and why doesn't any teacher teach that.... And how does sine inverts any value spit out a ratio of op/hyp .... What is the process of calculation? ..and how can I do that for any angle and any trigonometric ratio?(tangent cosine etc etc)

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I'm not good when it comes to math and this probably doesn't answer your question but it looks cool and relates to what you're asking so hopefully it helps in some way. If not, carry on.

external link and higher quality version if it doesn't load: https://i.imgur.com/jbqK8MJ.gifv

 

emYIXoW.gif

 

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You're right, calculators can't just know the values of trig functions for every angle. Instead, they use approximations. According to a quick google they use something called the CORDIC algorithm but I don't know anything about that and if you're like 99% of people you probably won't understand what that Wikipedia article is going on about.

 

The more "classic" example is the Taylor Series, which essentially approximates any function (including a sine wave) as a polynomial (ie a sum of xn terms, i.e. a + bx + cx2 + dx3 +...). As the graphic at the top of the Wikipedia article shows, you don't really need that many terms for the approximation to be reasonably accurate between -pi and +pi radians (-180 and +180 degrees) which is all you need for a trig function.

 

Edit: Also, I should add, you should never be expected to calculate something obscure like sin(43deg) by hand. 0, 30, 45, 60, 90 degrees or one of those numbers in another quadrant - yes, and maybe some others you can easily do from reference angles if you use the correct angle addition/double angle formulae, but you shouldn't be asked to calculate sin(43deg) by hand.

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