To find the value of \(\cos 40^\circ\), we can use a calculator or computational tool. The cosine of \(40^\circ\) is approximately:
\[ \cos 40^\circ \approx 0.766 \]
Rounding this to the nearest hundredth gives:
\[ \cos 40^\circ \approx 0.77 \]
Thus, the final answer is:
\[ 0.77 \]