# Using Differentials to Approximate Tan 61

In this tutorial we shall look at the use differentials to approximate the value of $\tan {61^ \circ }$.

The nearest number to 44 whose tangent value can be taken is 61, so let us consider that $x = {60^ \circ }$ and $\delta x = dx = {1^ \circ }$.

Now consider

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

Taking the differential of equation (i), we have

Putting this value in equation (ii), we have