Boris M.

nth Term of a Sequence Find a formula for the $n$ th term of the sequence
$$
\sqrt{2}, \quad \sqrt{2 \sqrt{2}}, \quad \sqrt{2 \sqrt{2 \sqrt{2}}}, \quad \sqrt{2 \sqrt{2 \sqrt{2 \sqrt{2}}}}, \ldots
$$
[Hint: Write each term as a power of $2 . ]$

Is there only one way to evaluate $\cos \left(\frac{5 \pi}{4}\right)$ ? Explain how to set up the solution in two different ways, and then compute to make sure they give the same answer.

For the following exercises, find the exact value.
$$
\cos \left(\frac{7 \pi}{12}\right)
$$

For the following exercises, find the exact value.
$$
\sin \left(\frac{5 \pi}{12}\right)
$$

For the following exercises, find the exact value.
$$
\tan \left(-\frac{\pi}{12}\right)
$$

For the following exercises, rewrite in terms of $\sin x$ and $\cos x .$
$$
\sin \left(x+\frac{11 \pi}{6}\right)
$$