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

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

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.

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

For the following exercise,

Find the exact value.

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

For the following exercise,

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

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

Integrate

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

For the following exercise,

Find the exact value.

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

In this exercise, verify the identity.

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

For the following exercise,

Find the exact value of each trigonometric function.

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

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

Verify that each equation is an identity.

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

Find $y^{\prime}$.

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

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

For the following exercise,

Find the exact value.

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