If y = sin x and x changes from to, what is the approximate change in y?

Given y = sin x and x changes from to.

Let so that

On differentiating y with respect to x, we get

We know

When, we have.

Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as

Here, and

∴ Δy = 0

Thus, there is approximately no change in y.