# Trigonometry Classwork 5-23-17

In 1-9, solve each equation for $x$ such that $0\leq x<2\pi$.

1. $2\sin(3x)+1=0$
2. $2\cos(2x)+1=0$
3. $\sec(4x)-2=0$
4. $\sqrt{3}\tan(3x)+1=0$
5. $2\cos(3x)=1$
6. $2\sin{x}\tan{x}-\tan{x}=1-2\sin{x}$
7. $\sec{x}\tan{x}-\cos{x}\cot{x}=\sin{x}$
8. $\tan{x}-3\cot{x}=0$
9. $\tan(3x)+1=\sec(3x)$
10. Solve for $x$ such that $0\leq x<2\pi$ and round to the nearest thousandth: $\cos{x}=0.4$

# Trigonometry Homework #12 due 5-25

Solve each equation for $x$

1. $2\sin{x}=\sin^2{x}+\cos^2{x}$

2. $3\tan^2{x}=1$

3. $\tan{x}-\cot{x}=\frac{\sin{x}-\cos{x}}{\sin{x}}$

4. $\cos^2\frac{x}{5}=\frac{1}{2}$

5. $\csc\left(x+\frac{2\pi}{5}\right)=1$

6. $\sqrt{\frac{1-\cos\frac{x}{4}}{2}}=\frac{\sqrt{3}}{2}$

7. $\tan{x}\cos{x}=0$

8. $\tan{x}=\frac{\sin\frac{5\pi}{6}}{1+\cos\frac{5\pi}{6}}$

9. $\sec^2{x}+1=5$

10. $\ln[-\cos(4x)]=0$

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

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