# Using Differentials to Approximate Cos 44

In this tutorial we shall look at the use of differentials to approximate the value of $\cos {44^ \circ }$.

The nearest number to 44 whose cosine value can be taken is 45, so let us consider that $x = {45^ \circ }$ and $\delta x = dx = - {1^ \circ }$.

Now consider

Since $y = \cos x,\,\,\delta y \approx dy$, putting these values in equation (ii), we have

Taking the differential of equation (i), we have

Putting this value in equation (ii), we have