Question

A curve is represented by y = sin x. If x is changed from \[\frac{\pi}{3}\text{ to }\frac{\pi}{3} + \frac{\pi}{100}\] , 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 
\[= \sin \left( \frac{\pi}{3} + \frac{\pi}{100} \right) - \sin \frac{\pi}{3}\]
= 0.0157