Answer
$$\frac{{9\pi }}{4}{\text{radians}}$$
Work Step by Step
$$\eqalign{
& {405^ \circ } \cr
& {\text{We know that }}{{\text{1}}^ \circ } = \frac{\pi }{{180}}{\text{radians}}{\text{. }}\left( {{\text{see}}\,\,{\text{page 668}}} \right){\text{ Then}}{\text{,}} \cr
& {405^ \circ } = 405\left( {\frac{\pi }{{180}}} \right){\text{radians}} \cr
& {\text{multiplying}} \cr
& {405^ \circ } = \frac{{405\pi }}{{180}}{\text{radians}} \cr
& {405^ \circ } = \frac{{9\pi }}{4}{\text{radians}} \cr} $$