Section  Topic  To Do  Anticipated Completion Date  04.01 Angles and Their Measures Lesson (Section 4.1 of your text), Practice Problem,
Submitted Assignment Before 10/16/12
04.02 Trigonometric Functions of Acute Angles Lesson (Section 4.2 of your text), Practice Problem,
Submitted Assignment Before 10/16/12
04.03 Trig Functions: The Unit Circle Lesson (Section 4.3 of your text), Practice Problem,
Submitted Assignment Before 10/23/12
04.04 Trig Functions of Any Angle Lesson (Section 4.3 of your text), Practice Problem,
Submitted Assignment Before 10/23/12
04.05a Graphs of Sine and Cosine Functions Lesson (Section 4.4 of your text), Practice Problem,
Submitted Assignment Before10/30/12
04.05b Analyzing the Sine and Cosine Functions Project Before10/30/12 04.06 Graphs of Other Trig Functions Lesson (Section 4.5 of your text), Practice Problem,
Submitted Assignment Before10/30/12
04.07 Inverse Trigonometric Functions Lesson (Section 4.7 of your text), Practice Problem,
Submitted Assignment Before 11/6/12
04.08 Solving Problems with Trigonometry Lesson (Section 4.8 of your text), Practice Problem,
Submitted Assignment Before 11/6/12
04.09 Module Four Practice Test and Review  Complete the module three practice test, review, and then call your instructor Before 11/13/12 04.10 Module Four Test
Trigonometric Functions Show your work on your exam Before 11/13/12 04.11 Reflection and Discussion Submit a copy of your posted tip Before 11/13/12
...Teaching trigonometry using Empirical Modelling
0303417
Abstract
The trigonometric functions sin(x), cos(x) and tan(x) are relationships that exist between the angles
and length of sides in a rightangled triangle. In Empirical Modelling terms, the angles in a triangle
and the length of the sides are observables, and the functions that connect them are the definitions.
These welldefined geometric relationships can be useful when teaching GCSElevel students about
the functions, as they provide a way to visualise what can be thought of as fairly abstract functions.
This paper looks at how different learning styles apply to Empirical Modelling, and presents a practical example of their use in a model to teach trigonometry.
1 Introduction
The trigonometric functions sin(x), cos(x) and tan(x)
are relationships that exist between the angles and
length of sides in a rightangled triangle. In Empirical Modelling terms, the angles in a triangle and the
length of the sides are observables, and the functions
that connect them are the definitions. These welldefined geometric relationships can be useful when
teaching GCSElevel students about the functions,
as they provide a way to visualise what can be
thought of as fairly abstract functions. Rather than
teaching students by showing them diagrams in an
instructive way (already a good way of doing it), a
constructive approach may allow students to gain a
better understanding...
...Trigonometry
 Introduction to trigonometryAs you see, the word itself refers to three angles  a reference to triangles. Trigonometry is primarily a branch of mathematics that deals with triangles, mostly right triangles. In particular the ratios and relationships between the triangle's sides and angles. It has two main ways of being used: 1. In geometryIn its geometry application, it is mainly used to solve triangles, usually right triangles. That is, given some angles and side lengths, we can find some or all the others. For example, in the figure below, knowing the height of the tree and the angle made when we look up at its top, we can calculate how far away it is (CB). (Using our full toolbox, we can actually calculate all three sides and all three angles of the right triangle ABC). 2. AnalyticallyIn a more advanced use, the trigonometric ratios such as as Sine and Tangent, are used as functions in equations and are manipulated using algebra. In this way, it has many engineering applications such as electronic circuits and mechanical engineering. In this analytical application, it deals with angles drawn on a coordinate plane, and can be used to analyze things like motion and waves. Chapter1Angles in the Quadrants( Some basic Concepts)In trigonometry, an angle is drawn in what is called the "standard position". The vertex of the angle is on the origin, and one side of the angle is fixed and drawn along the positive...
...Trigonometry (from Greek trigōnon "triangle" + metron"measure"[1]) is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology. Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of Hyperbolic geometry.


\History
Main article: History of trigonometry
The first trigonometric tablewas apparently compiled byHipparchus, who is now consequently known as "the father of trigonometry."[3]
Sumerian astronomers introduced angle measure, using a division of...
...Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology. Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of Hyperbolic geometry.
Contents
f one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees: they are complementary angles. The shape of a triangle is completely determined,...
...phones to school. It is very reasonable because bringing phone toschool potentially disrupts the learning process. Moststudents use cell phones irresponsibly. They use cell phones to talk to their friend during class time. They also use the calculator and camera features in the class as well. Those potentially lead less concentration in the time of learning and teaching process.
Students go to school to learn and behave fair way. Mobile phones provide a large temptation to cheat in tests. They can communicate to anyone and almost anywhere in the world. Because of the small size of the cell phone, students can send a text quietly and discreetly. The text can go unnoticed anywhere to get help on answering tests, homework, and other class assignment. Learning in school is to behave fair not cheating.
Therefore, schools should ban students from bringing their cell phones. However it should be done fairly. In case of an emergency some student need a call for help, providing easy access to phone is better.
NEVER TRY SMOKING
A lot of people, especially teenagers, who do not smoke,always want to try smoking. They know it is bad for them and all, but it is just something they want to try. So they ask one of their smoker friends for a cigarette. Admittedly, they firstly can not light it on their own so they ask his friend to do it. Then they inhale that cigarette and smoke occasionally.
Apparently that makes them the born smokers. Now they do smoke fairly...
...~TUDENTIDNO
FIRST TRIMESTER EXAMINATION, ZOO+2005 SESSION
PMT 0045  IT MATHEMATICS 1
( Alpha Information Technology studdnts only )
17 AUGUST 2004
9.00 a.m  11 .OO a.m
( 2 Hours )
INSTRUCTIONS TO STUDENT
1. This Question paper consists of 4 pages excluding the qover page and formula sheet.
2. Answer FOUR out of FIVE questions.
3. Please print all your answers in the Answer Booklet prcivided. All necessary working
MUST be shown.
Instruction: Answer FOUR questions only.
1 uestion
O
(a) Verify the identity
:
(b) Find the exact value of
cscBsinB =cotBcosB.
.
(
3 marks )
(
3 marks )
(c) If cosA =f with A in Quadrant I and cosB = i with B in Quadrant IV, find the
exact value of
0
cos(A + B)
ii)
sin 23
iii)
sin2
A
( 9 marks )
(d) Solve the equation 2 cos2 x  1 lcosx = 5,
0 < x c 27~
( 5 marks )
Continued.......
NilLCY/GWW
l/4
17 AUGUST 2004
IT MATHEMATICS I
PMT 0045
Ouestion 2:
(a) Solve A ABC, given a = 22 meters, b = 12 meters and A = 41’. Find the remaining
side and angles by using Law of Sines. Give your answer id two decimal places.
( 7 marks )
(b) Find the remaining angles and side of triangle below. Give tour answer in two
decimal places.
( 6 marks )
ii)
Convert from polar to rectangular coordinate for
( 7 marks )
Continued..
NIILCYIGWW
214
I
.....
Question 3:
(a) Find the equation of the parabola with focus at (2,5)...
...compiled by Hipparchus, who is now consequently known as "the father of trigonometry."[3]
Sumerian astronomers introduced angle measure, using a division of circles into 360 degrees.[4]They and their successors the Babylonians studied the ratios of the sides of similar triangles and discovered some properties of these ratios, but did not turn that into a systematic method for finding sides and angles of triangles. The ancient Nubians used a similar methodology.[5] The ancient Greeks transformed trigonometry into an ordered science.[6]
Classical Greek mathematicians (such as Euclid and Archimedes) studied the properties of chordsand inscribed angles in circles, and proved theorems that are equivalent to modern trigonometric formulae, although they presented them geometrically rather than algebraically. Claudius Ptolemyexpanded upon Hipparchus' Chords in a Circle in his Almagest.[7] The modern sine function was first defined in the Surya Siddhanta, and its properties were further documented by the 5th centuryIndian mathematician and astronomer Aryabhata.[8] These Greek and Indian works were translated and expanded by medieval Islamic mathematicians. By the 10th century, Islamic mathematicians were using all six trigonometric functions, had tabulated their values, and were applying them to problems in spherical geometry.[citation needed] At about the same time, Chinese mathematicians developed trigonometry independently, although it...
...Early trigonometry
The ancient Egyptians and Babylonians had known of theorems on the ratios of the sides of similar triangles for many centuries. But preHellenic societies lacked the concept of an angle measure and consequently, the sides of triangles were studied instead, a field that would be better called "trilaterometry".[6]The Babylonian astronomers kept detailed records on the rising and setting of stars, the motion of the planets, and the solar and lunar eclipses, all of which required familiarity with angular distances measured on the celestial sphere.[2] Based on one interpretation of the Plimpton 322 cuneiform tablet (c. 1900 BC), some have even asserted that the ancient Babylonians had a table of secants.[7] There is, however, much debate as to whether it is a table of Pythagorean triples, a solution of quadratic equations, or a trigonometric table.The Egyptians, on the other hand, used a primitive form of trigonometry for building pyramids in the 2nd millennium BC.[2] The Rhind Mathematical Papyrus, written by the Egyptian scribe Ahmes (c. 1680–1620 BC), contains the following problem related to trigonometry:[2]"If a pyramid is 250 cubits high and the side of its base 360 cubits long, what is its seked?"Ahmes' solution to the problem is the ratio of half the side of the base of the pyramid to its height, or the runtorise ratio of its face. In other words, the quantity he found for the seked is the cotangent of the...
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