Graphing the sin(theta) and cos(theta) using the Unit Circle

The Unit Circle is a circle with a radius of 1, and which is centered at the origin (0,0).
Its equation is: x² + y² = 1.
Its equation is also: x = cos(theta), y = sin(theta).
HOMEWORK part one: PROVE  to yourself that x² + y² = 1
for every point  in the following diagram. 

For example,

(1,0) ==> x = 1 and y = 0 ==>
          x^2 = 1 and y^2 = 0 ==> 1 + 0 = 1    check

(√3/2, 1/2) ==> x = √3/2 and y = 1/2 ==>
          x^2 = 3/4 and y^2 = 1/4 ==> 3/4 + 1/4 = 1   check

(√2/2, √2/2) ==> x = √2/2 and y = √2/2 ==>
          x^2 = 2/4 and y^2 = 2/4 ==> 2/4 + 2/4 = 1  check

and so on for all the points around the circle.

HOMEWORK part two: PLAY with the following applets
for the sin(theta) http://www.ies.co.jp/math/java/trig/graphSinX/graphSinX.html
and cos(theta) http://www.ies.co.jp/math/java/trig/graphCosX/graphCosX.html

and PROVE that sin(theta) = y and cos(theta) = x, for all the points
in the unit circle. Note, Don't forget to rotate the cos(theta) applet
after you have drawn it !

Ten minute TRIG from Victoria University (Australia)

Review the following formulas, write them out, and solve the problems on the following link:
http://www.staff.vu.edu.au/mcaonline/units/trig/ratios.html

Review the Pythagorean theorem again, and solve the problems on the following website: http://www.worsleyschool.net/science/files/pythagoras/pythagoreantheorem2.html

ENDOTHERMIC vs EXOTHERMIC chemical reactions

In endothermic reactions, the products have more energy than the reactants. Heat is absorbed from the surroundings (e.g., a cold pack).
In exothermic reactions, the products have less energy than the reactants. Heat is released to the surroundings (e.g., a heat pack).
Both reactions require some activation energy to begin the reaction.

Read the following section of Chemistry for Dummies, and write a summary of it: http://docs.google.com/Doc?docid=0ARNbGsVH1evCZGQ5MjluM2dfNzRxam13cXJuZw&hl=en , and make a diagram of an exothermic and an endothermic reaction.

Here is an example of the potential energy diagram for the following, exothermic chemical reaction:

CO + NO2 --> CO2 + NO

Decomposing vectors using TRIG

How can you decompose vectors into their components?
See this website to find out more:
http://www.sparknotes.com/testprep/books/sat2/physics/chapter4section5.rhtml

Solve the problems on this website for homework:
http://www.physics247.com/physics-homework-help/vector-components.php

stoichiometry -- balancing chemical equations using moles from the Chem Collective from Carnegie Mellon University

The following video gives the "big picture" of the mole and its applications.
The big picture of the mole from the Chem Collective from Carnegie Mellon University

Information on how to use the mole in balancing chemical equations is found here:
Stoichiometry: using the mole to balance chemical equations from The Chem Collective from Carnegie Mellon University

How far is Avogadro's number in meters? (6.023 x 10^23 m)

Avogadro's number...How big is it?
Can a person count to this number in their lifetime (counting once per second)?

How far away from the Earth would you be if you traveled this number of meters? See this video on youtube for an excellent, 9 minute description!
http://www.youtube.com/watch?v=A2cmlhfdxuY  Listen carefully to the video, and fill out this worksheet on google docs and answer the following questions: http://docs.google.com/Doc?docid=0ARNbGsVH1evCZGQ5MjluM2dfNzBkMzMydDNmdA&hl=en

Adding similar sine waves causes "BEATS"

What happens when you add similar sine waves together? Any musician can tell you: as you tune an instrument closer and closer to the correct tone, you start to hear "beats", when the tone sounds louder and softer and louder and softer and ... You get the idea.

What does it look like? Take a look.

 Ok, ok. I get it. What's the homework? Your job is to reproduce this sound, and draw it, using the following link: http://www.falstad.com/fourier/e-logsound.html
 and write a summary of what Beats are using the following article: http://en.wikipedia.org/wiki/Beat_%28acoustics%29

Blood tests are so complicated?

When you go to get a blood test, for what is the doctor looking? That depends on your age, gender, and symptoms. See the following website for all the details: http://en.wikipedia.org/wiki/Reference_ranges_for_common_blood_tests

Your job: to make a drawing of this graph and find at least 3 differences between men and women. Note! If you're using Google Chrome, you may need the latest plugin (it's safe to install).
You can also go to this site to get a printable version, but you **must** turn in your **own** diagram of this test. http://en.wikipedia.org/wiki/File:Blood_values_for_print.png

Making the (almost) perfect square wave. Can it be done?

Continue adding up sine waves until you get an almost perfect square wave.
Try changing the number of terms that make up the sum. Move the mouse over the sines/cosines to see each frequency's contribution to the sum.
Try also changing the playing frequency (with your computer's sound ON)
Go to this site: http://www.falstad.com/fourier/e-square.html

The pH of life

Note how narrow is the pH range of life for humans!
See this link on the effect of acid rain on the pH of lakes, and how this affects the fish's ability to survive:
http://www.lenntech.com/aquatic/acids-alkalis.htm