# What do the sine, cosine and tangent functions all do? [closed]

I know how to find the specific sides given by using $\sin x, \cos x,$ and $\tan x$, but what do these functions actually do, like when you say $\sin 43$, or $\cos 76$, or $\tan 29$?

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What do you mean when you ask "what does a function do"? You mean "what rule does it follow"? – Peter Tamaroff Feb 23 at 18:01
Did you look at the wikipedia articles on sine, cosine, and tangent? – Zev Chonoles Feb 23 at 18:02
The little robots in your calculator draw a rectangular triangle with $\alpha=43^\circ$, measure the corresponding sides of the triangle, calculate the quotient of their lengths and write down the reply in the display. (Being robots in a calculator, they use e-paper). – Hagen von Eitzen Feb 23 at 18:03

## closed as not a real question by Jim, Asaf Karagila, Davide Giraudo, Norbert, DidFeb 23 at 20:31

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.

We only know sin, cos, for some famous angles like 90,60,30,45 other than that we don't know but it is sometimes useful to use trig. identities to find values of other angles, for example we know that $$sin(x-y)=sinx(cosy)-(cosx)siny$$ this can be used to find $sin 15$ for example since $15=45-30$ and we know sin and cos for 45 and 30. other than this the only possible thing to do is approximation we know that $$sinx=\displaystyle \sum_{n=0}^{\infty} \frac{(-1)^{n}x^{2n+1}}{(2n+1)!}=x-\frac{x^3}{3!}+\frac{x^5}{5!}+...$$ since this sum is infinite we can choose some cut point lets say n=3 (the larger the cut point the more accurate your approximation) so we have $$sinx\approx x-\frac{x^3}{3!}+\frac{x^5}{5!}$$ so for example 43 in radians is $\frac{43\pi}{180}$ so let $x=\frac{43\pi}{180}$ and you'll get$$sin\frac{43\pi}{180}\approx 0.682$$ and if you used a calculater the first five digits are 0.68199, which is very close, and remember if we chose n is be larger say 10 the approximation will be better.

Remark: we also know some identities for $cosx$ and once we have $sinx$ and $cosx$ we can easily find $tanx$

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