For the following exercise,

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

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

Find $y^{\prime}$.

y=ln sec x

In this exercise, verify the identity.

$$\cos ^2 \frac{\theta}{2}=\frac{\sec \theta+1}{2 \sec \theta}$$

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: $1 \mathrm{~km} \approx 0.62 \mathrm{~mi})$

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

Integrate

$$\int \sec x \tan x d x$$

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

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

$$\csc 1$$

For the following exercise,

Find the exact value of each trigonometric function.

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

For the following exercise,

Find the exact value of each trigonometric function.

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

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

For the following, graph each side of the equation to find the zeroes on the interval $[0,2 \pi)$.

$$\sec ^2 x-2 \sec x=15$$

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

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