Converting Radians to Degrees (and vice versa )

Ok, I don't know why we have been avoiding this one.  Sorry.

There are 180 degrees in pi radians.  so rather than memorising foruma I start from there.

$$\begin{array}{rll}
180\;degrees &=& \pi\; radians\\\\
180\times \frac{50}{180} \;degrees &=& \pi \times \frac{50}{180} radians\\\\
50\; degrees &=& \pi \times \frac{5}{18} radians\\\\
50\; degrees &=& \frac{5\pi}{18}\; radians\\\\
\end{array}$$

By alpha of 400 degrees I assume you mean chantge 400 degrees to radians  

400-360=40degrees

$$\begin{array}{rll}
180\;degrees &=& \pi\; radians\\\\
180\times \frac{40}{180} \;degrees &=& \pi \times \frac{40}{180} radians\\\\
40\; degrees &=& \pi \times \frac{2}{9} radians\\\\
40\; degrees &=& \frac{2\pi}{9}\; radians\\\\
\end{array}$$