16 Use reference angles to find the exact value of the following expression. Do not use a calculator. $$ \begin{array}{l}\tan 780^{\circ} \ \text { Select the correct choice below and, if necessary, fill in the answer box to complete your choice. } \ \text { A. } \tan 780^{\circ}= \ \text { (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any } n \ \text { the denominator.) } \ \text { B. The answer is undefined. }\end{array} $$

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To find $$\tan 780^\circ$$, we first need to reduce the angle to an equivalent angle within the range of $$0^\circ$$ to $$360^\circ$$. We can do this by subtracting $$360^\circ$$ until we get an angle in that range.

1. Subtract $$360^\circ$$ from $$780^\circ$$:
   $$
   780^\circ - 360^\circ = 420^\circ
   $$
2. Subtract $$360^\circ$$ again:
   $$
   420^\circ - 360^\circ = 60^\circ
   $$

Now we have:
$$
780^\circ \equiv 60^\circ \quad (\text{mod } 360^\circ)
$$

Next, we can find $$\tan 60^\circ$$:
$$
\tan 60^\circ = \sqrt{3}
$$

Thus, the exact value of $$\tan 780^\circ$$ is:
$$
\tan 780^\circ = \sqrt{3}
$$

So the answer is:
$$
\text{A. } \tan 780^\circ = \sqrt{3}
$$
$$ \tan 780^\circ = \sqrt{3} $$

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