Question

The appropriate value is $\cos {61}^o$ is

• A. $0.4848$
• B. $0.4849$
• C. $0.4948$
• D. $0.5059$

Answer 1

The correct option is A $0.4848$

Let $y=\cos \left(x\right),x={60}^o$ and $x+△x={61}^o$

Where $x=\pi /3,\cos \frac{\pi }{3}=1/2$

then , $△x=1^o=0.01745$ radius

let $y=f\left(x\right)=\cos \left(x\right)$

differentiating wrt $x$,

$\frac{dy}{dx}=-\sin \left(x\right)\Rightarrow {\left(\frac{dy}{dx}\right)}_{x=\pi /3}=-\sin \left(\frac{\pi }{3}\right)=\frac{-\sqrt{3}}{2}$

Let $\Delta y$ be the change in $y$ due to change $\Delta x$ in $x$

$\therefore \Delta y=\frac{dy}{dx}\Delta x$.

$=\left(\frac{-\sqrt{3}}{2}\right)\left(0.01745\right)=-0.0151$

$\therefore f\left({61}^o\right)=y+△y=\frac{1}{2}-0.0151=0.1848$ Ans.