Question

Find the approximate value of $\cos ({89}^o,{30}^{\prime })$
[Given is : $1^o={0.0175}^{o}C]$

Answer 1

$\cos \left(89°{30}^{\prime }\right)f\left(x\right)=\cos xf\left(x\right)=-\sin xx=89°{30}^{\prime }=90°-{\left(\frac{1}{2}\right)}^{\circ }=a+ha=\frac{\pi }{2}h=-{\left(\frac{1}{2}\right)}^{\circ }=-\frac{0.0175}{2}=-0.00875f\left(a\right)=\cos \frac{\pi }{2}=0f^{{}^{\prime }}\left(a\right)=-\sin \frac{\pi }{2}=-1f(a+h)\approx f\left(a\right)+h{f}^{{}^{\prime }}\left(a\right)\approx 0-0.00875\times (-1)\approx 0.00875$