Lemuel Hackshaw
February 14th, 2013
MA122
History of Trigonometry
The History of Trigonometry dated back to the early ages of Egypt and Babylon. Many different Astronomers and Mathematicians all took place in helping create Trigonometry, people from Hipparchus, all the way to Isaac Newton. They all contributed a little something, something to formulate what we know as trigonometry. The places these events took place in different place like Greece and India, to Sweden to Germany. Trigonometry was formulated for computations in astronomy. A Greek Astronomer by the name of Hipparchus compiled the trigonometric table which measured the length of the chord subtending the various angles in a circle of a fixed radius r. In other words, Hipparchus made the first piece of the puzzle for the Unit Circle. His table was done in increasing degrees of 71.

Another man, buy the name of Ptolemy took that piece of the puzzle and created a table of chords which increased in 1 degree, this took place in the 5th century. This next piece was known as Menelaus’s theorem which formed the foundation of trigonometric studies for the next 300 years. Aroud that same time, an Indian mathematician took the chords out and replaced them with sine functions instead. This was a ratio, but rather the opposite of the angle in a right angle of fixed hypotenuse. A Muslim astronomer now compiled all of these ideas of both the Indians and the Greeks.

Now, in the 13th century, Germans made modern trigonometry by defining trigonometry functions as ratios rather than lengths of lines. Another Astronomer from Sweden discovered logarithms, and then another large step in Trigonometry was made by Isaac Newton whom founded differential and integral calculus. The history of Trigonometry came about mainly due to the purposes of time keeping and astronomy.

Four different careers that use trigonometry are Sailors, Astronomy, Architects, and Surveyors. Sailors use trigonometry for geography and...

...Pre-Calculus
Module 3
Chap. 7.1
2. If
8. Find
26. Find the remaining five trig functions of .
34. Match the columns.
38. Match the columns.
56. Write each expression in terms of sin and cosine, and simplify.
Chap 7.2
2. Perform each operation and simplify.
)cos
18. Factor each trig expression.
26. Use fundamental identities to simplify.
36. Verify is an identity.
46.
68.
I’m stumped on this one
84.
Chap 7.3
6. Use identities to find the exact value of
72. Write as a function of x.
106. Verify the identity of
Chap 7.4
20. Use an identity to write as a single trig function value or single number.
30. Express as a trig function of x.
56. Write each expression as a sum or difference of trig functions.
58. Write each expression as a product of trig functions.
72. Use the half angle identity to find the exact value.
112. Modeling Mach number.
Chap. 7.5
20. Find the exact value of each real number y.
)
28. )
38. Give the degree measure of .
)
62. Use a calculator to give each real number value.
80. Give the exact value of each expression w/o using a calculator.
94. Us a...

...Nick Latessa
Mrs. Schmalhofer
Pre AP Language Arts
25 April 2013
The Reasons Capital Punishment Should Stay Implemented
“When someone commits a felony, it is a matter of free will. No one is compelled to commit armed robbery, murder, or rape. The average citizen does not have the mind or intentions to become a killer(Ornellas).” This statement by Lori Ornellas, a victim in the brutal murder of her nephew shows us that when someone commits a crime they do it on their own account. In the United States today more than six thousand murder investigations a year go cold or go unsolved(Rein). This means that there are so many murders that get away and are not held accountable for the crimes that they have committed. Today in our society capital punishment is a form of punishment that is implemented in our justice system. Capital punishment should stay implemented in our justice system because, the death penalty can serve as a deterrent for violent crimes, the death penalty is morally permissible in today’s society, and under our Constitution the death penalty legally permissible.
In our country’s justice system the death penalty is good for many things, such as, serving as a deterrent for violent crimes all over the nation. We as humans have the ability to decide for ourselves whether an idea is good or bad. Often times to do this we look at the actions of others to earthier strengthen our confidence in our idea or to deter the idea that we have. This is...

...No 1. 2. 3. 4. 5. 6. 7. 8. Code: UCCM1153 Status: Credit Hours: 3 Semester and Year Taught:
Information on Every Subject Name of Subject: Introduction to Calculus and Applications
Pre-requisite (if applicable): None Mode of Delivery: Lecture and Tutorial Valuation: Course Work Final Examination 40% 60%
9. 10.
Teaching Staff: Objective(s) of Subject: • Review the notion of function and its basic properties. • Understand the concepts of derivatives. • Understand linear approximations. • Understand the relationship between integration and differentiation and continuity. Learning Outcomes: After completing this unit, students will be able to: 1. describe the basic ideas concerning functions, their graphs, and ways of transforming and combining them; 2. use the concepts of derivatives to solve problems involving rates of change and approximation of functions; 3. apply the differential calculus to solve optimization problems; 4. relate the integral to the derivative; 5. use the integral to solve problems concerning areas.
11.
12.
Subject Synopsis: This unit covers topics on Functions and Models, Limits and Derivatives, Differentiation Rules, Applications of Differentiation and Integrals.
13.
Subject Outline and Notional Hours: Topic Learning Outcomes 1 L 4 T 1.5 P SL 6.25 TLT 11.75
Topic 1: Functions and Models
• • • • • • Functions Models and curve fitting Transformations, combinations, composition and...

...Kristen Darling
Mr. Tumin
AP Calculus
11/8/12
Pharmacokinetics
According to the Medical dictionary the definition of “Pharmacokinetics is, sometimes abbreviated as PK, the word coming from Ancient Greek pharmakon "drug" and kinetikos "to do with motion,” is a branch of pharmacology dedicated to the determination of the fate of substances administered externally to a living organism. The substances of interest include pharmaceutical agents, hormones, nutrients, and toxins.” Pharmacokinetics is the study of the rate of drug absorption and disposition in the body. So, differential calculus is an important part in the development of many of the equations used.
There are four pharmacokinetic processes to which every drug is subject in the body: Absorption, Distribution, Metabolism, and Excretion
Absorption is the process by which a drug is made available to the fluids of distribution of the body. (i.e. blood or plasma) Most orally-administered drugs reach a maximum or peak level blood concentration within 1-2 hours.
Once a drug has been absorbed from the stomach and/or intestines into the blood, it is circulated to some degree to all areas of the body to which there is blood flow and that is the process of distribution. Metabolism is the complex of physical and chemical processes occurring within a living cell or organism that are necessary for the maintenance of life. In metabolism some substances are broken down to...

...1. Calculus is split into two branches, differential calculus and integral calculus. Differential calculus is used to find the rates of change for geometric curves. This means that differential calculus is used to find the slope or tangent along a specific direction of a geometric curve. This relates directly to change, because finding the slope or tangent of a geometric curve is essentially finding the rate of change for that geometric curve. The other branch of calculus, integral calculus, is concerned with finding the area under a curve. This is accomplished by using small towers, to find the closest area of the curve. This relates to change because you can find the difference in area of the curve, depending on the equation’s curve’s restrictions. The relationship between these two branches is that they are inverse operations. This means that taking a derivative after finding an integral, would leave you with the original equation.
2. The method of exhaustion is a process that is still used today in order to find the area of irregular shapes that typically have curved bounded areas. The process uses regular polygons to approximate the area of irregular polygons. This is done by the process of circumscription, which means that a regular polygon is placed around the irregular polygon, but each of the corners of the regular polygon will touch the edge of the circle....

...Calculus
is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integralcalculus (concerning accumulation of quantities and the areas under curves); these two branches are related to each other by the fundamental theorem ofcalculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-definedlimit. Calculus has widespread uses in science, economics, and engineering and can solve many problems that algebra alone cannot.
Calculus is concerned with comparing quantities which vary in a non-linear way. It is used extensively in science and engineering since many of the things we are studying (like velocity, acceleration, current in a circuit) do not behave in a simple, linear fashion. If quantities are continually changing, we need calculus to study what is going on.
BRANCHES OF CALCULUSCalculus is concerned with comparing quantities which vary in a non-linear way. It is used extensively in science and engineering since many of the things we are studying (like velocity, acceleration, current in a circuit) do not behave in a simple, linear fashion. If...

...SOLUTIONS TO SUGGESTED PROBLEMS FROM THE TEXT PART 2
3.5 2 3 4 6 15 18 28 34 36 42 43 44 48 49 3.6 1 2 6 12 17 19 23 30 31 34 38 40 43a 45 51 52 1 4 7 8 10 14 17 19 20 21 22 26 r’(θ) = cosθ – sinθ 2 2 cos θ – sin θ = cos2θ z’= -4sin(4θ) -3cos(2 – 3x) 2 cos(tanθ)/cos θ f’(x) = [-sin(sinx)](cosx) -sinθ w’ = (-cosθ)e y’ = cos(cosx + sinx)(cosx – sinx) 2 T’(θ) = -1 / sin θ x q(x) = e / sin x F(x) = -(1/4)cos(4x)
(a) dy/dt = -(4.9π/6)sin(πt/6) (b) indicates the change in depth of water (a) Graph at end (b) Max on 1 July; 4500; yes; 1 Jan (c) pos 1 April; neg 1 Oct (d) 0 2 2 2 (a) a cosθ + √l – a sin θ (b) i: -2a cm/sec 2 2 2 ii: -a√2 – a / (√l – a /2 cm/sec
28 36 37 42 52a 52b 1 2 4b 5 8 13 17 26a 29 39 41 1 2 3 17 22 29 36 44a 46 49 2 5 8 10 14 16b 21 25 26 27 5.2 1 6 8 10 14
Sketch at end Sketch at the end
x = 0: not max/min x = 3/7: local max x = 1: local min
4.2
-1/3 g decreasing near x = x0 g has local min at x1 Sketch at end Sketch at end x = 4; y = 57
Max: 20 at x = 1 Min: -2 at x = -1; x = 8 Max: 2 at x = 0; x = 3 Min: 16 at x = -1; x = 2 (a) f(1) local min; f(0), f(2) local max (b) f(1) global min; f(2) global max
Global min = 2 at x = 1, No global max D=C r = 3B/(2A) Sketch at end Sketch at end. x = L/2 x = 2a Min: -2amps; Max: 2 amps
(a) xy + πy /8 (b) x + y + πy/2 (c) x = 100/(4 + π); y = 200/(4 + π)
2
2t / (t + 1) 1 / (x – 1) cosα/sinα (lnx) + 1 e . 1/x 1 -sin (lnt) / t 2 2 / (√1 – 4t ) 1 / t lnt 2 1 / (1 + 2u + 2u ) 0.8 -1 ‹ x ‹ 1 1 / ((ln...