After you have finished constructing the spaghetti sine curve, answer the following questions.

What is the radius of the circle? 5in

What is the circumference of the circle? 2πr=2(π)(5)=31.4

At what degree measure on your circle would you find the angle correponding to 375°? 15 degrees What is the term for the angle you found in question #3? reference angle

After how many degrees does the graph start to repeat? 360 degrees This is the period of the graph and corresponds to one complete wave – a wavelength.

What is the height of the triangle (spaghetti) at 30 degrees? Compare this to the radius (that it, find the ratio: [pic]and make it a decimal). 2.5/5=.5 On the calculator find the sine of 30º: .5 How does that compare to your answer above for [pic]?

it is the same
What is the height of the triangle at 150° and 330°? 2in. How does this compare with the height of the 30° angle in #6 above? it is the same.

What is the height of the triangle at 45°, 135°, 225°? 3.5in. Make a ratio of for these angles like you did in #6: 3.5/5=.7 On the calculator find the sine of 45°: .707 Compare this to your answer to question #9.

this is very close
If you were to explain to a person who has never seen trigonometry what the sine of an angle is, what would you tell them?

I would tell them that it is the side opposite of the angle over the hypotenuse which is the radius of the circle.

12. What do you think is the significance of reference angles?
If you know the main reference angles than you can use that information to find other angles on the circle. -----------------------
Name_______________________________Per._____

Draw the x and y axis on your circle.
With a protractor put a mark every 15° and extend these marks from the origin to the edge of the circle. Take a string and wrap it carefully around the circumference of your circle. Put a mark on the string at all of your 15° intervals. Take the string and...

...Rogers Muldrow
11/18/2012
AP English III
Period VI
Flying Spaghetti MonsterAnalysis
As soon as one begins to read The Essay on The Flying Spaghetti Monster, they can infer that it is a paradoy. The essay uses the technique of puns with the name of “Pastafarians”, and exaggeration with the Global Warming Graph, but the main technique used was sarcasm.The entire essay was a sarcastic attempt to show that Intellegent Design (Creationism) isnt a legitament science with any kind of “backbone” or factual data making it inappropiate to teach in schools. It is showing that by comparing Christianity and Pastafarianism. The essay states, “If the Intelligent Design is not based on Faith, but instead another scientific theory, as is claimed, then you must also allow our theory to be taught, as it is also based on science, not on faith.” What that means is that Christianity was going to given the right to be taught as a science in school, and both Pastafarianism and Christianity both have the same amount of proof, which means that Pastafarianism should also have the same right to be taught in school.
At first sight it may seem like comparing Jesus Christ, or God to a “Flying Spaghetti Monster”, is making a mockery of the religion or taking an insult too far, but this step needed to be taken in order for the point to be made. The author needed to take this extra step in order for the radicals of...

...
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...Physics IA
A factor affecting Spaghetti
Jonathan Dean
Scotch College
28/03/13
Design
Introduction
The aim of this experiment will be to conduct an investigation into a factor of spaghetti. Such factors include how the diameter will relate to the flexibility of the spaghetti, or how the carbohydrate content will relate to the flexibility. For this experiment, the carbohydrate content and how it relates to the flexibility will be investigated.
Flexibility will be determined by the angle the spaghetti can subtend before it breaks.
Research question
What is the relationship between the carbohydrate content of spaghetti and the flexibility of the spaghetti?
Variables
* The independent variable: The carbohydrate content of spaghetti
* The dependant variable: The angle of flexibility before the spaghetti breaks
* The controlled variables will include:
* The diameter of the spaghetti
The diameter of the spaghetti will need to be kept constant as the flexibility of spaghetti will alter with a changing diameter. With a greater diameter it follows that the spaghetti will be stronger, therefore will not flex as much.
* Length of the spaghetti
The length of the spaghetti will affect its flexibility. A longer piece of spaghetti...

...Spaghetti sauce and pasta – Regular Recipe
Ingredients:
2 lbs. Italian sausage, casings removed (mild or hot)
1 small onion, chopped (optional)
3 -4 garlic cloves, minced
1 (28 ounce) can diced tomatoes
2 (6 ounce) cans tomato paste
2 (15 ounce) cans tomato sauce
2 cups water (for a long period of simmering for flavors to meld. If you don't want to simmer it as long, add less)
3 teaspoons basil
2 teaspoons dried parsley flakes
1 1/2 teaspoons brown sugar
1 teaspoon salt
1/4-1/2 teaspoon crushed red pepper flakes
1/4 teaspoon fresh coarse ground black pepper
1/4 cup red wine (a good Cabernet!)
1 lb. thin spaghetti
parmesan cheese
Directions:
1. In large, heavy stockpot, brown Italian sausage, breaking up as you stir.
2. Add onions and continue to cook, stirring occasionally until onions are softened.
3. Add garlic, tomatoes, tomato paste, tomato sauce and water.
4. Add basil, parsley, brown sugar, salt, crushed red pepper, and black pepper.
5. Stir well and barely bring to a boil.
6. Stir in red wine.
7. Simmer on low, stirring frequently for at least an hour. A longer simmer makes for a better sauce, just be careful not to let it burn!
8. Cook spaghetti according to package directions.
9. Spoon sauce over drained spaghetti noodles and sprinkle with parmesan cheese....

...Tracy Gitonga
Modeling Data With Trigonometric Functions
Precalculus 1113-213
October 18, 2011
Real-life math is used in many activities that people do in a daily basis. In the next few paragraphs I will be explaining how to use a real world data and model it with a sine function of the form of y= a sin K (x-b). The graphs will use the law of sine which is defines as, “a law stating that the ratio of the sine of an arc of a spherical triangle to the sine of the opposite angle is the same for all three arcs.”
The following table gives the number of hours of daylight in Philadelphia, Pennsylvania.
Day | | Mar 21 | Apr 21 | May 21 | | June 21 | | July 21 | | Aug 21 | | Sept 21 | | Oct 21 | | Nov 21 | | Dec 21 |
Hours of Day-light | | 12 | 13.7 | 14.2 | | 14.8 | | 14.2 | | 13.7 | | 12 | | 11.4 | | 9.8 | | 9.2 |
While plotting the data, I realized that the sine function works better because the graph begins from the point (0) on the x-axis of the graph. Firstly, I realized I need to be able to find my equation before formulating a graph. My equation is y= a sin K (x-b). I need to find the “a”, which stands for amplitude, “the maximum extent of a vibration or oscillation, measured from the position of equilibrium.” I took the difference between the highest and lowest daylight hours reading in the table and divided by two.
14.8 – 9.2 = 5.6/2
A= 2.8
Secondly, I figured the period which is defined as, “a space of...

... Choice, Happiness, and Spaghetti Sauce was a well thought-out brain teaser type of video. Author and writer Malcom Gladwell introduces the audience to the food industry’s pursuit of the perfect spaghetti sauce, but ends up making a larger argument about the nature of choice and happiness in a comical yet intelligent manor on TEDTalk. Gladwell uses his friend and Psychophysicist Howard Moskowitz’s crazy idea with Pepsi, and breakthrough formula for success with Vlasic Pickles and Prego spaghetti sauce to expose diversity, variability, and finding the true meaning of happiness. Based on the company’s Dr. Moskowitz worked for and inspired, this video has shown me some personal changes in my life that need to be changed.
The whole purpose of Gladwell’s speech was based on one specific quote, “Embracing the diversity of human beings is the way we will find true happiness” (Gladwell). When we the people learn to accept and not judge the fact that all humans are different; only then will be we able to understand ourselves. Gladwell goes in depth with several scenarios that Dr. Moskowitz experienced in the food industry to help back up this theory; which in time he learned from Dr. Moskowitz himself. The very first company to approach Dr. Moskowitz was Pepsi. Being a Psychophysicist, “person who measures things” (Gladwell), Pepsi came to Dr. Moskowitz in hopes of finding out how much Aspartame they needed to put in their sodas to make...

...assignments I missed, the lack of my time management, and the goals I have set for myself in the future.
My final grade in Trigonometry for the Fall Term was a 61%. I do not believe this score truly represents my ability. I believe this because I procrastinated and clowned around a lot of the time. For example: I would wait until the day before the test to start studying, I later on learned that this tool is not made for success. Another example: I would joke around with my classmates all the time even when they were trying to work, then I realized this tool is not a good tool for success.
There are many assignments that I failed to complete; Assistment: Probability & Data Analysis Review, Assistment: Unit 1 LT1, Wendy’s Letter, Assistment: Trig Unit 2: LT1, Assistment Unit 2 Quiz, Assistment: Unit 2 LT9 HW, Assistment: Unit 3 LT4 HW, Assistment: Unit 4 Pre Assessment, Parent Signed Grade Report, Unit 4 LT1 LT2 LT3 Notes, Assistment: Reviewing Units 1-3, Part 1 Turned In On Time, Design Challenge - Part 1, Design Challenge - Part 2, Part 2 Turned In On Time, Assistment: Unit 4 Pretest, Unit 4 Pretest Corrections, and Final Assistment HW: Semester Reflection.
Along with incompletions I also had many non-masteries; Unit 1: LT1 - LT4 Quiz, Unit 2 Test, Assistment: Unit 3 Review Quiz, Unit 3 Test, Unit 3 Mastery Project, Unit 5 LT1 Quiz 1, Unit Circle Quiz, Unit 5 Calculator Test, Unit 5 No Calculator Test, Unit 6 Test, Final Exam Review Presentation,...

...inverses, we take the interval -π2 to π2, which contains all the possible values of the sine function. Now, the new domain is [-π2, π2], while the range stays the same. We then switch the domain and the range, so the domain and range of arcsin (x) is [-1,1] and [-π2, π2]. For cosine, the interval [0,π] contains all possible values, and the range is still [-1,1]. To find arcos (x) we invert the domain and range again, to get [-1,1] as the domain and [0,π] as the range. For arctan (x), the interval (-π2, π2) includes all possible values. The range still remains all real numbers. Exchanging the domain and range gives us all real numbers as the domain and (-π2, π2) as the range.
As you can see, the properties of the six trig functions have many similarities and the inverse trig functions’ domain and range can be obtained with the one to one property of inverse functions...