Question

A curve is represented by $y=\sin x.$ If $x$ is changed from $\frac{\pi }{3}$ to $\frac{\pi }{3}+\frac{\pi }{100},$ find approximately the change in $y.$

Answer 1

$y=\sin x$

The change in the value of $y$ can be obtained as:

So, $y+\Delta y=\sin (x+\Delta x)$

$\Delta y=\sin (x+\Delta x)-\sin x$

$=(\frac{\pi }{3}+\frac{\pi }{100})-\sin \frac{\pi }{3}=0.0157$.

$y_2-y_1=\Delta y=0.0157$