Find $y^{\prime}$.

y=ln sec x

Find $y^{\prime}$.

$$y=e^{x \sec x}$$

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.

$$\csc 1$$

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

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.)

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

$$\tan 3.4$$

Graph the function.

y=1+sec x

For the following exercise,

Find the exact value of each trigonometric function.

$$\sin \frac{\pi}{2}$$

Verify that each equation is an identity.

$$\cos 2 \theta=\frac{2-\sec ^2 \theta}{\sec ^2 \theta}$$

Jesse drove from Los Angeles to Las Vegas, a distance of $463 \mathrm{~km}$. He used $12 \mathrm{gal}$ of gas on the trip. Find the gas mileage in miles per gallon of Jesse's car. (Hint: $1 \mathrm{~km} \approx 0.62 \mathrm{~mi})$

For the following exercise,

Find the exact value.

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

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