Step 1 :To find the value of \(\cos (-t)\), we need to remember that the cosine function is an even function, which means that \(\cos (-t) = \cos (t)\).
Step 2 :Since we are given that \(\cos t=\frac{4 \sqrt{5}}{9}\), we can directly use this value for \(\cos (-t)\).
Step 3 :\(\cos (-t) = \frac{4 \sqrt{5}}{9}\)
Step 4 :Final Answer: \(\boxed{\frac{4 \sqrt{5}}{9}}\)