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

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

For the following exercise,

Find the exact value.

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

For the following exercise,

Find the exact value.

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

In this exercise, verify the identity.

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

Find $y^{\prime}$.

y=ln sec x

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.

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

For the following exercise,

Find the exact value of each trigonometric function.

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

Find $y^{\prime}$.

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

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

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

$$\tan 3.4$$

For the following exercise,

Find the exact value of each trigonometric function.

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

For the following exercise,

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

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