Please help solve cos 65 ° . What will be the easiest way to go for evaluation of cos 65 ! I proceeded like cos (45+20) expanded and then for stuck at value of sin20 and cos20 . How will i get it ?
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$\begingroup$I would write $\cos 65=\cos(60+5)=\cos 60 \cos 5 - \sin 60 \sin 5 \approx \frac 12-\frac {\sqrt 3}2 \frac {\pi}{36}$ where the error is less than $\frac 12(1-\frac 12 \cos 5) \approx\frac 12\cdot\frac12(\frac{\pi}{36})^2\approx \frac {10}{5200}\lt .002$ The basic idea is to find an angle that is close for which you know the sine and cosine, then expand the difference in a Taylor series.
$\endgroup$ $\begingroup$What topics are you covering in class at the moment?
If you are doing Taylor expansions, perhaps just work out the Taylor expansion for cos(65).
Alternately, since 65 = 60 + 5, you could use the cosine addition formula to work out cos(60 + 5). Since 5 is pretty small, you could make an approximation to simplify your work for cos(5).
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