# Calculus Homework #11 due 5-18

Given the graph of $f(x)$ above, calculate the following definite integrals.

1. $\int_{-3}^{-5}f(x)dx$
2. $\int_2^4f(x)dx$
3. $\int_{-3}^3f(x)dx$
4. $\int_3^2f(x)dx$

# Trigonometry Homework #11 due 5-18

Prove each identity.

1. $\cos^4\theta-\sin^4\theta=\cos(2\theta)$
2. $\sin(4x)=4\sin{x}\cos{x}\cos(2x)$
3. $\frac{\sin(2x)}{1+\cos(2x)}=\tan{x}$
4. $\cot\alpha+\tan\alpha=2\csc(2\alpha)$
5. $\tan(\pi-\alpha)=-\tan{\alpha}$

# Trigonometry Classwork 5-9

1. What is the equation of this function?

2. What is the equation of this function?

3. Graph $y=\frac{\arctan{x}}{\pi}+1$

4. Graph $y=2\csc{x}+3$

5. Graph $y=\frac{3\sin\left (2\left (x-\frac{\pi}{8}\right )\right )}{2}-2$

# Trigonometry Homework #10 Due 5-11

Match each graph with its equation.

a. $y=\arctan{x}+\pi$

b. $y=\tan{x}-2$

c. $y=4\cos\left (\frac{x-\pi}{2}\right )+4$

d. $y=\cos(\pi(x+1))$

e. $y=\arccos{x}+\pi$

f. $y=\tan\left (\frac{x-\pi}{2}\right )+2$

g. $y=\sec\left (\frac{x-\pi}{2}\right )+2$

h. $y=2\sin\left (2\left (x-\frac{\pi}{3}\right )\right )-1$

i. $y=\csc\left (x+\frac{\pi}{6}\right )-1$

j. $y=\cot\left (\frac{\pi}{2}\left (x-\frac{1}{2}\right )\right )+1$

k. $y=\frac{\sec(\pi{x})}{2}$

l. $y=\frac{\sin\left (2\left (x-\frac{\pi}{3}\right )\right )}{2}-1$

m. y=arcsec(x+1)

n. $y=\arccos(x+2)$

o. $y=2\sin{x}-1$

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

# Calculus Homework #10 Due 5-11

1. A rectangle has a vertex on the $x$-axis between 0 and 9, a vertex at the point (9,0), a vertex on the line $x=9$, and a vertex on the curve $y=\sqrt{x}$. Find the dimensions of the rectangle having the maximum possible area.

2. To get the best view of the Statue of Liberty you should be at the position where $\theta$ is a maximum. If the statue stands 92 meters high, including the pedestal, which is 46 meters high, how far from the base should you be?

3. You run a small furniture business. You sign a deal with a customer to deliver some number of chairs, the exact number to be determined by the customer later. The price will be $90 per chair up to 300 chairs, and above 300, the price will be reduced by$0.25 per chair (on the whole order) for every additional chair over 300 ordered. What is the maximum amount of money your company can make on this order?

4. For which positive number $x$ is $x^{\frac{1}{x}}$ largest?

# Trigonometry Project #2: Tides & Functions

For this project, your task is to come up with an equation that models the height of the water in Dutch Kills as a function of time.

To do this, you will need to collect lots of data! Because of this, groups may share data. Think about what data you’ll need to collect and what a good plan for collecting it is.

The project is due by the end of the day on Friday, June 2nd

You will be evaluated primarily on the accuracy of your equation and on your description of your process. You also must include the data collected either as a table or a scatter plot or both. An excellent project will include an equation for a function that comes within an hour and within a foot of each data point and an explanation of how you applied knowledge of trigonometric graphs and transformations to fit the function to the data.

# Trigonometry Homework #9 due 5-4

Graph the following functions.

1. $y=\sec\left[\frac{1}{2}\left(x+\frac{\pi}{3}\right)\right]$

2. $y=2\sec{x}+3$

3. $y=\frac{\csc(\pi{x})}{2}$

4. $y=\csc\left(x-\frac{\pi}{4}\right)$

5. $y=\cot(2\pi{x})-1$