Question:
A curve is represented by $\mathrm{y}=\sin \mathrm{x}$. If $\mathrm{x}$ is changed from $\frac{\frac{\pi}{3}}{\tan } \frac{\pi}{3}+\frac{\pi}{100}$, 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 $\mathrm{y}=\mathrm{y} 2-\mathrm{y} 1=\sin (\pi / 3+\pi / 100)-\sin (\pi / 3)$
$=\sin (\pi / 3+(\pi / 3+\pi / 100-\pi / 3))-\sin (\pi / 3)$
$=0.0157$
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