Question

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

Answer 1

y = sin x ...(i)



Now, consider a small increment ∆x in x.
Then y + ∆y = sin (x + ∆x) ...(ii)
Here, ∆y is the small change in y.

Subtracting (ii) from (i), we get:
∆y = sin (x + ∆x) − sin x
$=\sin \left(\frac{\mathrm{\pi }}{3}+\frac{\mathrm{\pi }}{100}\right)-\sin \frac{\mathrm{\pi }}{3}$
= 0.0157