61. TheMathPage  Topics In Trigonometry trigonometry from the very beginning. trigonometry. Home. These pages are intended to be seen in Garamond with Internet Explorer 5 or Netscape 6. http://www.themathpage.com/aTrig/trigonometry.htm

var sc_project=798906; var sc_partition=6; var sc_security="32e508b6"; Home These pages are intended to be seen in Garamond font with Internet Explorer 6, or the equivalent. THE TOPICS Ratio and Proportion Radicals: Rational and Irrational Numbers The Pythagorean Theorem ... Home Questions or comments? E-mail: themathpage@nyc.rr.com . Please do not sent attachments.

62. Expression Calculator Performs over a hundred simple, and complex calculations, with the ability to make several calculations simultaneously. Functions range from simple trigonometry, to Gaussian integrals, through 2D plots. Win95/98/Me/NT/2000 http://excalc.vestris.com/

Expression Calculator will dazzle you with its simplicity and power of over 100 mathematical expressions, its multithread capabilities and its complete documentation with historical references, algorithms and more. Expression Calculator version 2.43 for Windows XP, 2000, NT, 95/98 Introducing the Expression Calculator The history of the calculator, references and more. Download the Expression Calculator Shareware and registered versions. Users Guide and Reference Adobe PDF format (zipped) Complete reference of all functions with historical notes, definitions and items of interest. Register the Expression Calculator Paying for a License By registering, you will be able to download the full version of the Expression Calculator with 3D plots, financial functions and more. Screenshots from the Calculator What's New FREE! 15 days trial Quick Download back to Vestris Inc. site Vestris Inc

63. Topics In Trigonometry:  Trigonometry Of Right Triangles trigonometry from the very beginning. PLANE trigonometry IS BASED on the fact of similar figures. (Topic 1 Ratio and proportion.) We saw http://www.themathpage.com/aTrig/trigonometry-of-right-triangles.htm

The Topics Home TRIGONOMETRY OF RIGHT TRIANGLES Similar figures All functions from one function Complements Cofunctions Similar figures P LANE TRIGONOMETRY IS BASED on the fact of similar figures. (Topic 1: Ratio and proportion .) We saw: Figures are similar if they are equiangular and if the sides that make the equal angles are proportional. Right triangles will be similar, however, simply if an acute angle of one triangle is equal to an acute angle of the other. ( Theorem 14 .) Thus in the right triangles ABC, DEF, if the acute angle at B is equal to the acute angle at E, then those triangles will be similar. The sides that make the equal angles will be proportional. If CA is half of AB, for example, then FD will also be half of DE. To be more specific, if angle every sides will be in the same ratio. A trigonometric Table is a table of ratios of sides. In the Table, each value of sin is the ratio of the opposite side to the hypotenuse in every right triangle having that angle. Thus we read in the Table Example. Indirect measurement.

64. Mathematics Problem Writing Service For School, Math Leagues Mathematics problems for middle school and high school math competitions with topics range from algebra and geometry to probability and trigonometry. http://www.virtu-software.com/math/

Math Competition Problem Writer Quality Mathematics Problems For High School and Middle School Competitions One of the great ways to inspire students to learn more about mathematics is to hold competitions in which students compete against students from their own school, or from around the state, or country. Problem solving skills are sharpened, while teamwork is encouraged. The end result is that students think more critically, understand concepts better, and learn to work well together. Douglas Twitchell, who maintains Virtu Software's Problem Of the Week page, experienced this first hand throughout his elementary, secondary, and college career. Twitchell is a former competitor and award winner in a variety of state and national math competitions. He has won awards and recognition in leagues such as MAML, NEML, ASMA, NEAML, and in college he ranked in the top 150 in the prestigious William Lowell Putnam exam. In recent years, he has been hired by various mathematics leagues, such as the Maine Association of Math Leagues, the Maine Algebra and Geometry League, and others, to write creative and challenging math problems for middle school and high school mathematics competitions. Whether it's a regional, state, or school competition, consider hiring Doug to write problems for your math meet. The problems are carefully crafted and written, with diagrams where appropriate, all cleanly formatted for printing. Each problem is proofed to guarrantee both accuracy and clarity. Proofing is done by a high school math teacher and math team coach, and the proofing cost is included.

65. Trigonometry - Wikipedia, The Free Encyclopedia trigonometry (from the Greek trigonon = three angles and metro = measure) is The origins of trigonometry trace to the cultures of the ancient Egyptians http://en.wikipedia.org/wiki/Trigonometry

Trigonometry From Wikipedia, the free encyclopedia. Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles triangles and trigonometric functions such as sine cosine and tangent . It has some relationship to geometry , though there is disagreement on exactly what that relationship is; for some, trigonometry is just a subtopic of geometry. edit Early history The origins of trigonometry trace to the cultures of the ancient Egyptians and Babylonians and Indus Valley civilizations, over 3000 years ago. Indian mathematicians were the pioneers of variable computations algebra for use in astronomical calculations along with trigonometry. Lagadha is the only known mathematician today to have used geometry and trigonometry for astronomy in his book Vedanga Jyotisha, much of whose works were destroyed by foreign invaders on India. Greek mathematician Hipparchus circa 150 BC compiled a trigonometric table for solving triangles. Another Greek mathematician, Ptolemy circa 100 AD further developed trigonometric calculations. The Silesian mathematician Bartholemaeus Pitiscus published an influential work on trigonometry in and introduced the word to the English and French languages.

66. S.O.S. Math - Trigonometry Covers measuring degrees, equations, and formulas. Includes illustrations and related links. http://www.sosmath.com/trig/trig.html

S.O.S. Homepage Algebra Calculus Differential Equations ... CyberBoard Search our site! S.O.S. Math on CD Sale! Only $19.95. Works for PCs, Macs and Linux. Tell a Friend about S.O.S. Books We Like Math Sites on the WWW S.O.S. Math Awards ... Privacy Concerns? TRIGONOMETRY Angle Measures Trigonometric Functions The magic identity The Addition Formulas ... SOLVING TRIGONOMETRIC EQUATIONS CALCULUS AND TRIGONOMETRY The Derivatives of Trigonometric Functions HYPERBOLIC TRIGONOMETRY The Hyperbolic Functions The Inverse Hyperbolic Functions Contact us Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA users online during the last hour

67. Trigonometric Functions Chapters of Copernicus s book giving all the trigonometry relevant to This contained work on planar and spherical trigonometry originally done much http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Trigonometric_functions.h

The trigonometric functions Analysis index History Topics Index Version for printing The use of trigonometric functions arises from the early connection between mathematics and astronomy. Early work with spherical triangles was as important as plane triangles. The first work on trigonometric functions related to chords of a circle. Given a circle of fixed radius, 60 units were often used in early calculations, then the problem was to find the length of the chord subtended by a given angle. For a circle of unit radius the length of the chord subtended by the angle x was 2sin ( x /2). The first known table of chords was produced by the Greek mathematician Hipparchus in about 140 BC. Although these tables have not survived, it is claimed that twelve books of tables of chords were written by Hipparchus . This makes Hipparchus the founder of trigonometry. The next Greek mathematician to produce a table of chords was Menelaus in about 100 AD. Menelaus worked in Rome producing six books of tables of chords which have been lost but his work on spherics has survived and is the earliest known work on spherical trigonometry. Menelaus proved a property of plane triangles and the corresponding spherical triangle property known the regula sex quantitatum.

68. TheMathPage:  Skill In Arithmetic  Topics In Trigonometry Arithmetic and trigonometry courses taught at Borough of Manhattan Community College, The City University of New York. http://www.themathpage.com/

var sc_project=798906; var sc_partition=6; var sc_security="32e508b6"; j="1"; j="3"; A complete course. A complete course. Trigonometry from the beginning. From the ratio of natural numbers to the need for irrational numbers. E-mail: themathpage@nyc.rr.com

69. Trigonometry - Content Standards (CA Dept Of Education) Grades Eight Though Twelve Mathematics Content Standards. http://www.cde.ca.gov/be/st/ss/mthtrig.asp

Search Advanced Site Map A-Z Index Professional Development ... Printer-friendly version Trigonometry Grades Eight Though Twelve - Mathematics Content Standards. Trigonometry uses the techniques that students have previously learned from the study of algebra and geometry. The trigonometric functions studied are defined geometrically rather than in terms of algebraic equations. Facility with these functions as well as the ability to prove basic identities regarding them is especially important for students intending to study calculus, more advanced mathematics, physics and other sciences, and engineering in college. Students understand the notion of angle and how to measure it, in both degrees and radians. They can convert between degrees and radians. Students know the definition of sine and cosine as y- and x- coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions. Students know the identity cos (x) + sin (x) = 1: 3.1 Students prove that this identity is equivalent to the Pythagorean theorem (i.e., students can prove this identity by using the Pythagorean theorem and, conversely, they can prove the Pythagorean theorem as a consequence of this identity).

70. Science In India: History Of Mathematics: Indian Mathematicians And Astronomers, Describes Indian mathematicians such as Aryabhatta who modelled the solar system, Bhaskar, Varahamira, and others who made important contributions in the fields of trigonometry, algebra, and classical analysis. http://members.tripod.com/~INDIA_RESOURCE/mathematics.htm

setAdGroup('67.18.104.18'); var cm_role = "live" var cm_host = "tripod.lycos.com" var cm_taxid = "/memberembedded" Search: Lycos Tripod Dukes of Hazzard Share This Page Report Abuse Edit your Site ... Next SOUTH ASIAN HISTORY Pages from the history of the Indian sub-continent: Science and Mathematics in India History of Mathematics in India In all early civilizations, the first expression of mathematical understanding appears in the form of counting systems. Numbers in very early societies were typically represented by groups of lines, though later different numbers came to be assigned specific numeral names and symbols (as in India) or were designated by alphabetic letters (such as in Rome). Although today, we take our decimal system for granted, not all ancient civilizations based their numbers on a ten-base system. In ancient Babylon, a sexagesimal (base 60) system was in use. The Decimal System in Harappa In India a decimal system was already in place during the Harappan period, as indicated by an analysis of Harappan weights and measures. Weights corresponding to ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500 have been identified, as have scales with decimal divisions. A particularly notable characteristic of Harappan weights and measures is their remarkable accuracy. A bronze rod marked in units of 0.367 inches points to the degree of precision demanded in those times. Such scales were particularly important in ensuring proper implementation of town planning rules that required roads of fixed widths to run at right angles to each other, for drains to be constructed of precise measurements, and for homes to be constructed according to specified guidelines. The existence of a gradated system of accurately marked weights points to the development of trade and commerce in Harappan society.

71. Trigonometry Review trigonometry Review. Definitions of Trigonometric Functions. You need a Javaenabled browser to take this quiz. Values of Functions in the First Quadrant http://www.batesville.k12.in.us/Physics/CalcNet/Trig_Review/Trig_Review.html

Trigonometry Review Definitions of Trigonometric Functions You need a Java-enabled browser to take this quiz. Values of Functions in the First Quadrant You need a Java-enabled browser to take this quiz. Trigonometric Identities You need a Java-enabled browser to take this quiz. last update August 25, 1998 by JL Stanbrough

72. All Elementary Mathematics - Online Mathematical School... An online mathematical high school. Arithmetic, algebra, geometry, trigonometry, functions and graphs, analysis. Theory and solving problems. Also has practice exams and math jokes. http://www.bymath.com

Math symbols Jokes Forum About us ... Site map Citizenship In the Mathematics Country! This site is an online mathematical high school where you can study without leaving your home (online education). This site unlike others contains all necessary information of elementary mathematics in full measure. Here You’ll Find Everything: · theory · problems · help · tests · consulting · reference · None of other sites can be compared to this site by width and profundity of the mathematics curriculum consideration. So, if you want to understand and fall in love with elementary mathematics, if you like to master it perfectly and to solve any math problems and to enter any university, then come on! The Site Is For You! Sitting in front of the computer, you'll be able to fulfill any math homework, to raise your marks at school and to comprehend the curriculum of the high school. You'll feel that there are no secrets in mathematics for you. The site will answer all your questions, be your consultant and assistant in studying, it is real preparatory school. Here you'll find necessary information and be able to deepen your knowledge in all basic sections of elementary mathematics: arithmetic, algebra, geometry, trigonometry, functions and graphs, principles of analysis and so on. You'll be ready to pass any mathematical tests and exams. The site is conducted by a scientist and a professor experienced in preparing students for the best universities. He is cognizant of the all levels of the mathematics curriculum.

73. Gainesville College Math Tournament For Two-Year Colleges Held in the spring of each year, the competition features both individual and team events involving problems from calculus, trigonometry, geometry, statistics, and algebra. http://www.gc.peachnet.edu/math/tournament/

74. StudyWorks! Online : Interactive Trig Examine the sine function graphically! Six Trig Functions Six Trig Functions A guide to the six basic functions of trigonometry. http://www.studyworksonline.com/cda/explorations/main/0,,NAV2-23,00.html

Algebra Explorations Astronomy Biology Chemistry ... Sports Interactive Trig The activities in this section will help you get a "hands-on" feel for some of the fundamental principles of trigonometry. Note: These activities are all based on Java applets which may take a few moments to download if you are connecting by modem. Please be patient. Cos(t)=a Find the angle that satisfies the equation cos(t) = a, when a is given. Learn how to transform the graph of sin(x) using the equation , and see the effects of changing the values of a, b, and c. Graph of cos(x) See how the graph of y = cos(x) is created. Graph of sin(ax) See how to graph y = sin(ax) in this interactive activity. Graph of sin(x) See how to create the graph of y = sin(x). Graph of tan(x) Learn how to create the graph of y = tan(x). Sin(t)=a Find the angle that satisfies the equation sin(t) = a when a is given. Sine Function Box Examine the sine function - graphically! Six Trig Functions A guide to the six basic functions of trigonometry.

75. Trigonometry Worksheets trigonometry Using a calculator (sin, cos, tan) trigonometry Mixed Review. More trigonometry Find the exact value of one trigonometric function given a http://www.edhelper.com/trigonometry.htm

Return to edHelper.com Return to Math Trigonometry Worksheets Trigonometry Using a calculator (sin, cos, tan) Using a calculator (inverse functions) Find the tangent of one point Tangent: Find the value of x ... Trigonometry Mixed Review More Trigonometry Find the exact value of one trigonometric function given a point Find the exact value of six trigonometric functions given a point Gives quadrant and one trigonometric function Find the exact value for each trigonometric function ... Mixed Review Have a suggestion or would like to leave feedback? Leave your suggestions or comments about edHelper!

76. Mathematics Reference trigonometry identities and calculus rules for integration and differentiation. http://www.alcyone.com/max/reference/maths/index.html

Mathematics reference Ma MathRef A mathematics reference for students and teachers. Conventions. Mathematics reference: Notation A unified mathematical notation used throughout these pages. Ma Trigonometric identities and properties. Mathematics reference: Trigonometric identities Various identities and properties essential in trigonometry. Ma Mathematics reference: Hyperbolic trigonometry identities Various identities essential in hyperbolic trigonometry. Ma Differential and integral calculus. Mathematics reference: Limits Properties of limits. Ma Mathematics reference: Rules for differentiation Essential rules for differentiation. Ma Mathematics reference: Rules for integration Essential rules for integration. Ma Vectors and matrices. Mathematics reference: Rules for vectors Basic properties of vectors. Ma Mathematics reference: Rules for matrices Basic properties of matrices. Ma Navigation. Erik Max Francis TOP Welcome to my homepage. e Reference UP A technical reference. Re Mathematics reference: Notation START A unified mathematical notation used throughout these pages. Ma Quick links.

77. History Of Mathematics - Table Of Contents Topics include background in Babylonian, Euclid, Al'Khwarizmi, pi, and trigonometry. Also has recreations and java chat. http://members.aol.com/bbyars1/contents.html

And Insights into the History of Mathematics Table of Contents Prologue The First Mathematicians The Most Famous Teacher Pi: It Will Blow Your Mind ... Comments and Notices

78. Trigonometry Comments to Jim Reed. Started September, 1998. Copyright © 1999, 2000, 2001, 2002, 2003, 2004. Hit Counter visitors since April 15, 2002. http://argyll.epsb.ca/jreed/math9/strand3/trigonometry.htm

Comments to: Jim Reed visitors since April 15, 2002

79. Mathematics Learn how to use expressions to represent numbers, work with variables and create special drawings to represent equations. Also has a brief introduction to trigonometry and curve fitting. Includes interactive graphs. http://id.mind.net/~zona/mmts/mmts.html

More Mathematics than Science Science Contents Index Home ... E-mail

80. Trigonometry And Music trigonometry and Music. Sounds are produced by things that vibrate. Pure tones, like the the sounds produced by tuning forks, are described by sine waves y http://www.csm.astate.edu/music.html

Trigonometry and Music Sounds are produced by things that vibrate. Pure tones, like the the sounds produced by tuning forks, are described by sine waves y = A sin(2 pi f t), where t is time, f is how many times the thing is vibrating per second (f is for frequency , and A is how loud the sound is (A is for amplitude). If something is vibrating 256 times a second, you hear middle c. Sound of middle c (.wav file) Here is the graph. You can see that there are about, well, 25.6 waves during one tenth of a second. If we show you one second in the same amount of space, it just looks like a blob. If we double the frequency of any tone, we go up exactly one octave. So 512 vibrations per second is c above middle c. C above middle c (.wav file) Here is the graph. We get more complex sounds by adding waves of different frequencies and loudnesses together. A violin string or an oboe cavity will vibrate with more than one frequency at once, usually at multiples of a fundamental frequency. Here is a wave with components at 512 Hertz, 1024 Hz, 1536 Hz and 2048 Hz (1 Hz = 1 vibration per second). Sound of this wave The higher components are called harmonics of the fundamental tone. If the fundamental is c at 512 Hertz, then the second harmonic is twice the frequency, c an octave higher at 1024 Hertz, the third harmonic is g at 1536 Hertz, and the fourth harmonic is c at 2048 Hertz. A musical tone consists of the fundamental and many harmonics added together.

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