For the following exercise,

Find the exact value of each trigonometric function.

$$\cos \frac{\pi}{6}$$

Show how you would synthesize 2-phenylhex-3-yn-2-ol, starting with acetophenone $\left(\mathrm{PhCOCH}_{3}\right)$ and any other reagents you need. (“2-ol” means there is an OH group on C2.)

For the following exercise,

Find the exact value.

$$\cos \left(\frac{7 \pi}{12}\right)$$

Karl ralses his hand and Informs Ms. Rhombi that he has discovered another property related to the angles of an inscribed quadrilateral. He claims that the measure of any exterior angle of the quadrilateral is equal to the measure of the opposite interior angle in the quadrilateral. In other words, $m \angle A W Z=m \angle Y$. Explain Karl's reasoning.

For the following exercise,

Let $f(x)=\frac{3}{5} \cos (6 x)$.

What is the smallest possible value for $f(x)$?

For the following exercise,

Find the exact value.

$$\sin \left(\frac{7 \pi}{8}\right)$$

For the following exercise,

Find the exact value.

$$\sec \left(\frac{3 \pi}{8}\right)$$

In this exercise, use a calculator to find the value of the trigonometric function to four decimal places.

$$\tan 3.4$$

How many electrons does it take to have a total charge of - 1 C?

What are the products of reaction of (E)-3-methyl-3-hexene with each of the reagents in the indicated problem?

In this exercise, solve for the value of x that will satisfy the given equation.

$${ }_6 P_2=x\left({ }_5 P_3\right)$$

In this exercise, find the exact value of the following trigonometric function:

$$\cos \frac{2 \pi}{3}$$

Solve each equation for x, where x in [0, 2pi].

a) sec x csc x - 2 csc x = 0

b) 3 sec ^2 x - 4 = 0

c) 2 sin x sec x - 2 square root of 3 sin x = 0

d) 2 cot x + sec^2 x = 0

e) cot x csc^2 x = 2 cot x

f) 3 tan^3 x - tan x = 0

Consider a right rectangular prism:

a. Edge AF is perpendicular to (makes right angles with) which of these? (The bar notation is common for line segments.)

edge FE, or $\overline{F E} \quad$ edge AD, or $\overline{A D} \quad$ edge AB, or $\overline{A B}$

segment AG, or $\overline{A G} \quad$ segment BF, or $\overline{B F} \quad$ segment FH, or $\overline{F H}$

b. Name the endpoints of three edges that are parallel to edge AD.