# Trig Identity Homework due 5-7-14 (MRS22-3) or 5-8-14 (MRS22-1)

Prove each identity.

1. $\frac{\cot\theta}{\csc\theta}=\cos\theta$

2. $\cos^{2}x\tan^{2}x=\sin^{2}x$

3. $\frac{1-\sin^{2}\beta}{\cos\beta}=\cos\beta$

4. $\frac{\tan^{2}\alpha+1}{\sec\alpha}=\sec\alpha$

5. $1-\csc{x}\sin^{3}x=\cos^{2}x$

6. $\cos^{2}\theta(\tan^{2}\theta+1)=1$

7. $\sin^{2}\beta(1+\cot^{2}\beta)=1$

8. $\cot\theta+\tan\theta=\csc\theta\sec\theta$

9. $\sin^{2}\alpha+\tan^{2}\alpha+\cos^{2}\alpha=\sec^2\alpha$

10. $1+\csc^{2}x\cos^{2}x=\csc^{2}x$

# Calculus Homework Due 4-24-14

1. Find the exact global minimum value of $f(x)=x+\frac{1}{x}$ on the domain $\{x|x>0\}$

2. Find the exact global minimum and maximum values of $g(t)=te^{-t}$ on the domain $\{t|t\geq0\}$

3. A certain quantity of gas occupies a volume of 20cc at a pressure of 1 atmosphere. The gas expands without the addition of heat, so, for some constant $k$, its pressure, $P$, and volume, $V$, satisfy the equation $PV^{1.4}=k$. (a) Find the rate of change of pressure with respect to volume. (b) The volume is increasing at 2cc/min when the volume is 30cc. At that moment, is the pressure increasing or decreasing? How fast?

4. (a) A hemispherical bowl of radius 10cm contains water to a depth of $h$cm. Find the radius of the surface of the water as a function of $h$. (b) The water level drops at a rate of 0.1 cm per hour. At the what rate is the radius of the water decreasing when the depth is 5 cm?

# Tides & Functions Project

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, April 25th.

Here are the groups:

MRS22-1

• Oliwia K., Jade, Gabriel, Jonathan
• Kamil, Chris, Ignacio, Suraya
• Margaret, Myles, Prova, Rebecca
• Olivia L., Ashley, Lukasz, Andrew
• Auri, Cameron, Judah, Theo
• Saarah, Clofie, Kate, Julia

MRS22-3

• Hanaa, Raissa, Dominique
• Larry, Akash, Jim
• Valen, Tajreen, Christian
• Jetsun, Revana, Emily