# Using Differentials to Approximate Csc 61

In this tutorial we shall develop the differentials to approximate the value of $\csc {61^ \circ }$.

The nearest number to 61 degrees whose cosecant value can be taken is 60 degrees, so let us consider that $x = {60^ \circ }$ and $dx = {1^ \circ } = \frac{\pi }{{180}} = 0.0174$.

Now consider

Differentiating equation (i) with respect to $x$, we have

Taking the differential of equation (ii), we get

Using the values $x = {60^ \circ }$ and $dx = 0.0174$, we have

Now