Without a calculator, how can I calculate the sine of an angle, for example 32(without drawing a triangle)?
$\endgroup$ 42 Answers
$\begingroup$You can use first order approximation $\sin(x+h)=\sin(x)+\sin'(x)h=\sin(x)+\cos(x)h$
where $x$ is the point nearest to $x+h$ at which you already know the value of the $\sin$ function and its derivative $\cos$ function too.
Like for $\sin(32^0)=\sin(30^0)+\cos(30^0)*(\frac{\pi}{90})$
Here you need to take $h$ in radians which is $\frac{\pi}{90}$ for $(32^0-30^0)=2^0$
$\endgroup$ $\begingroup$Using Taylor expansion you get an approximation up to the desired precision
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