Solve the following :

Question:

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

Solution:

$y=\sin (x)$

Let $y 1=\sin (\pi / 3)$ and $y 2=\sin (\pi / 3+\pi / 100)$

Change in $y=y 2-y 1=\sin (\pi / 3+\pi / 100)-\sin (\pi / 3)$

$=\sin (\pi / 3+(\pi / 3+\pi / 100-\pi / 3))-\sin (\pi / 3)$

$=0.0157$

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