61. Cool Math Lessons - Trigonometry - The Pythagorean Identities math sites math for kids math for ages 13100 algebra lessons teachers math area parents math area math games Science Monster Spike s Game http://www.coolmath.com/pythagoreanidentities.htm

Your browser does not support the IFRAME tag. The Pythagorean Identities Your browser does not support the IFRAME tag. This page shows the derivations of the three Pythagorean Identities. A "derivation" means that we need to create this from scratch - or, at least, from other things that we know. Let's start with the Unit Circle: Zooming in to get a better look, we can label the sides of our right triangle... By the Pythagorean Theorem, we have that Since this is a Unit Circle, we have Substituting, gives us (The first Pythagorean Identity) Most people easily remember this first identity... But, often times, you'll need to remember the other two when you get to Calculus. Here's an easy way to derive the next two, starting from the first one: 2) Divide everywhere by Simplifying gives us the second Pythagorean Identity... 3) Divide everywhere by Simplifying gives us the third and final Pythagorean Identity...

62. Trigonometry: A Day At The Track This property is perhaps the most important it is saying that the behavior of these trigonometric functions is periodic . In other words, the functions http://www.ugrad.math.ubc.ca/coursedoc/math100/notes/zoo/trig.html

Rates of Growth Derivatives of Trigonometric functions UBC Calculus Online Course Notes Trigonometry: A day at the track Let's suppose we are watching a foot race and while watching the runners, our minds turn in a mathematical direction. Let's focus on one of the runners as she runs in a counter-clockwise direction about the circular track. She is wearing a blue hat as she runs at a constant speed. The picture below shows what we might see from three vantage points. We have three observers who can record her position. One is a photographer directly overhead, in the sponsor's blimp, and two others are on the ground in the bleachers at the East (E) and South (S) end of the track. The photographer in the blimp sees the picture shown above. However, the two observers on the ground see her running past, first one way and then the other. Each one of them can only see a one-dimensional view of her motion, and it might look as though she is bouncing back and forth, like a ping-pong ball. You might think that what these two ground observers are seeing is quite similar. Indeed, in many ways the picture that they see is the same, but they see it at different times. This is what we call a

63. Mathwords: Index For Trigonometry Index for trigonometry Math terminology from triangle trig, circle trig. Includes material about trig functions, their inverses, and trig identities. http://www.mathwords.com/index_trig.htm

index: click on a letter A B C D ... A to Z index index: subject areas sets, logic, proofs geometry algebra trigonometry ... entries www.mathwords.com about mathwords website feedback Index for Trigonometry Math terminology from triangle trig, circle trig. Includes material about trig functions, their inverses, and trig identities. Alpha Amplitude Angle of Depression Angle of Elevation ... Wavelength this page updated 2-apr-08 Mathwords: Terms and Formulas from Algebra I to Calculus written, illustrated, and webmastered by Bruce Simmons

64. Trigonometry From the inner (dot) product, employing the synthetic method, in this online textbook, we develop the elementary geometries (including the trigonometry), http://www.rism.com/Trig/Trig02.htm

Elementary-Geometry Trigonometry Abstract From the inner (dot) product, employing the synthetic method, in this online textbook, we develop the elementary geometries (including the trigonometry), in a pseudo-metrizable topology. The hyperbolic and circular trigonometric functions on a complex space are defined in terms of the exponential function. Their inverses are obtained. The addition theorems are presented and inverted. The derivatives, integrals, and infinite expansions are obtained. The Raphson, Newton, and Horner methods of finding the roots of an equation are presented. The binomial theorem and Gamma function are presented, also. Synthetic Geometry does not employ a coordinate system; it develops the congruence and similarity theorems. Analytic Geometry employs coordinate systems. It is happy to make use of the congruence or similarity theorems; but usually does not prove them. We employ the Synthetic Geometry, exclusively. The same distinction may be made between Analytic Vector Analysis vs.

65. All Elementary Mathematics - Study Guide - Trigonometry ... Radian and degree measures of angles. Transforming of degree measure to radian one and back. Trigonometric functions. Solving of rightangled triangles. http://www.bymath.com/studyguide/tri/tri_topics.html

Home Math symbols Jokes Forum ... Site map Program of Lessons T r i g o n o m e t r y Radian and degree measures of angles Transforming of degree measure to radian one and back Trigonometric functions of an acute angle Solving of right-angled triangles ... Dr. Yury Berengard

66. Differentiation Of Trigonometry Functions These rules follow from the limit definition of derivative, special limits, trigonometry identities, or the quotient rule. In the list of problems which http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/trigderivdirectory/TrigDeriv

DIFFERENTIATION OF TRIGONOMETRY FUNCTIONS In the following discussion and solutions the derivative of a function h x ) will be denoted by or h x ) . The following problems require the use of these six basic trigonometry derivatives : These rules follow from the limit definition of derivative, special limits, trigonometry identities, or the quotient rule. In the list of problems which follows, most problems are average and a few are somewhat challenging. On problems 1.) through 8.) find answers WITHOUT using the chain rule. PROBLEM 1 Differentiate Click HERE to see a detailed solution to problem 1. PROBLEM 2 Differentiate Click HERE to see a detailed solution to problem 2. PROBLEM 3 Differentiate Click HERE to see a detailed solution to problem 3. PROBLEM 4 Differentiate Click HERE to see a detailed solution to problem 4. PROBLEM 5 Differentiate Click HERE to see a detailed solution to problem 5. PROBLEM 6 Differentiate Click HERE to see a detailed solution to problem 6. PROBLEM 7 Differentiate Click HERE to see a detailed solution to problem 7.

67. Trigonometry - Mathematics And The Liberal Arts Discusses how Ptolemy may have constructed his trigonometry tables, which in effect give a table of sines for every quarter degree between 0o and 90o http://mtcs.truman.edu/~thammond/history/Trigonometry.html

Trigonometry - Mathematics and the Liberal Arts To expand search, see Geometry . Laterally related topics: Symmetry Analytic Geometry Pattern Geometric Theorems ... Tilings , and The Square The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews , published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet Brendan, Brother T. How Ptolemy Constructed Trigonometry Tables. Mathematics Teacher Discusses how Ptolemy may have constructed his trigonometry tables, which in effect give a table of sines for every quarter degree between

68. Earliest Uses Of Symbols For Trigonometric And Hyperbolic Functions Cajori writes that perhaps the first use of abbreviations for the trigonometric lines goes back to Finck (Cajori vol. 2, page 150). http://members.aol.com/Jeff570/trigonometry.html

Earliest Uses of Symbols for Trigonometric and Hyperbolic Functions Last revision: Sept. 12, 2007 Sine. In 1583, Thomas Fincke (or Finck) used sin. (with a period) in Book 14 of his Geometria rotundi. Cajori writes that "perhaps the first use of abbreviations for the trigonometric lines goes back to ... Finck" (Cajori vol. 2, page 150). In 1624, Edmund Gunter (1581-1626) used sin (without a period) in a drawing representing Gunter's scale (Cajori vol. 2, page 156). However, the symbol does not appear in Gunter's work published the same year. In 1626, Girard designated the sine of A by A, and the cosine of A by a (Smith vol. 2, page 618). In a trigonometry published by Richard Norwood in London in 1631, the author states that "in these examples s stands for sine t for tangent sc for sine complement tc for tangent complement sc for sine complement tc for tangent complement sec for secant " (Smith vol. 2, page 618). In 1632, William Oughtred (1574-1660) used sin (without a period) in Addition vnto the Vse of the Instrvment called the Circles of Proportion (Cajori vol. 1, page 193, and vol. 2, page 158).

69. Trigonometry Angle Calculator - Online Interactive Visual Triangle Calculator trigonometry angle calculator Online interactive visual software. Square, triangle, sphere, pie tank and cylinder angles area and volume. http://www.visualtrig.com/

Triangles Circles Angles Polygons Trigonometry Calculator Tell a friend! Bookmark This Site! Enter values for any 2 sides (yellow) or any 1 side and 1 angle, and click Calculate to re-draw triangle Thickness Volume 0.8 m³ Area 8 m² We know: Base = 4000 and Rise = 4000 So: Diagonal = √( 4000² + 4000² ) Top Angle = arctan(4000 / 4000) Bottom Angle = arctan(4000 / 4000) Triangle Rectangle The Triangle has a Base of 4,000, a Rise 4,000, a Diagonal 5,657 with Top angle of 45° and Bottom angle of 45° and an Area of 8 m² Degrees Radians Precision Trigonometry Calculator Need help to learn Trigonometry? These interactive calculators can help you learn triangle geometry by drawing shapes and displaying formulas as you enter angles, side lengths and depths etc. The Triangle Calculator redraws the triangle, displaying formulas for any set of entered side or angle combinations. The Circle and Tank Calculator redraws the circle, displaying all measurements and angles, volumes and areas. You can see the shapes, angles, lengths and trigonometric functions and formulas in the results Print Your Own Raflle Tickets!

70. Illuminations Trigonometry For Solving Problems This lesson offers a pair of puzzles to enforce the skills of identifying equivalent trigonometric expressons. Addtional worksheets enhance students http://illuminations.nctm.org/LessonDetail.aspx?id=L383

71. Trigonometry - Library Of Math Smith, David A. trigonometry From Library of Math Online math organized by subject into topics. http//www.libraryofmath.com/trigonometry.html http://www.libraryofmath.com/trigonometry.html

Trigonometry about trigonometry trigonometry learning trigonometry angle graph trig functions ... related pages Cite this as: Trigonometry Published by Library of Math Online math organized by subject into topics. Written by Smith, David A. http://www.libraryofmath.com/trigonometry.html google_ad_client = "pub-5291523068777517"; google_ad_slot = "6582858805"; google_ad_width = 468; google_ad_height = 60; Library of Math Online Math Organized by Subject Into Topics Online Math about mathematics abstract algebra one analytic geometry ... trigonometry google_ad_client = "pub-5291523068777517"; google_ad_slot = "5630916950"; google_ad_width = 336; google_ad_height = 280; Math Books abstract algebra business math calculus ... vocational math google_ad_client = "pub-5291523068777517"; google_ad_slot = "5630916950"; google_ad_width = 336; google_ad_height = 280; Custom math gifts on sale now. Share your enthusiasm for mathematics! Math Gifts Be Happy Do Math I Love Math Math Teachers ... Prime Time The Library of Math - Online Math Organized by Subject Into Topics about us feedback mision statement help var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E"));

72. Study Trigonometry Welcome to the trigonometry community where you can find helpful learning modules (Cramlets™), study sheets, tutorials, and helpful articles in the http://www.college-cram.com/study/trigonometry/

Better Grades in Less Time Browse Tag cloud Help Log on: Username  Password  Remember me You're Here: Trigonometry Tags RSS Feeds Trigonometry's Blog Community blog Weblog Archive Friends blog Members of This Community Rudy Mark Ragnar •un Derek Morton ... Members Trigonometry's Files File Storage (0 files) Trigonometry's Notebook Notebook Entries Choose a Subject to Study! Accounting Business Math ... Trivia Study Trigonometry Extended profile Click here to view extended profile Interests arctangent cosine functions hypotenuse ... triangle This page is Sponsored by: Trigonometry Notebook Pick a Trigonometry Chapter to Study - angle functions trigonometric function graph complex numbers Introduction trigonometry notebook . Take the time to connect with other learners, the content, and with learning about trigonometry. If you are good at trigonometry and would like to contribute notes, study sheets, or your own presentations then join up and post away! Advertise with us This ad could be yours! About Us Latest Buzz ... Press Professor Cram's Notebooks: Accounting Business Math Economics Finance ... The Smartacus Corporation and contributing members as provided in our Terms and Conditions var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E"));

73. Algebra II: Trigonometry - Math For Morons Like Us Math for Morons Like Us Algebra II trigonometry. http://library.thinkquest.org/20991/alg2/trig.html

Systems of Eq. Polynomials Frac. Express. Complex Numbers ... Trig. Identities On this page we hope to clear up problems you might have with the trigonometric ratios. The trigonometric ratios are very useful when dealing with triangles and unit circles. Click any of the links below or scroll down to better your understanding of the trigonometric ratios. Ratios (sin, cos, tan) Reciprocal ratios (csc, sec, cot) Rotations (unit circle) Radians Cofunctions Graphs involving the trig. ratios Pythagorean and quotient identities Algebraic manipulation Quiz on Trigonometry The trig. ratios, sine cosine , and tangent are based on properties of right triangles. The function values depend on the measure of the angle. The functions are outlined below. sine x = (side opposite x )/hypotenuse cosine x = (side adjacent x )/hypotenuse tangent x = (side opposite x )/(side adjacent x In the figure below, sin A = a/c, cosine A = b/c, and tangent A = a/b. There are two special triangles you need to know, 45-45-90 and 30-60-90 triangles. They are depicted in the figures below. The figures show how to find the side lengths of those types of triangles. Besides knowing how to find the length of any given side of the special triangles, you need to know their trig. ratio values (they are always the same, no matter the size of the triangle because the trig. ratios depend on the measure of the angle). A table of these values is given below.

74.   Mathematics :: Trigonometry A site where Electrical Engineering, Technology and High School students can analyze electronic circuits and math problems online. http://www.analyzethat.net/trigonometry_3.php

User: Login In About Us Sign Up Demos ... Mathematics :: Trigonometry Solving the Area of the Right Triangle Solving the Area of the Oblique Triangle Solving the Area of Equilateral Triangle Solving the Area of a Square ... Privacy Policy

75. BUBL LINK: Trigonometry Includes formulae relating to algebra, calculus, trigonometry, differential equations, and complex variables. Listings of the first 1000 prime numbers, http://bubl.ac.uk/link/t/trigonometry.htm

BUBL LINK Catalogue of Internet Resources Home Search Subject Menus Countries ... Z Trigonometry Titles Descriptions Finite Mathematics and Applied Calculus Resource Page Introduction to Trigonometry Mathematics Archives Name Project Trigonometry ... WebMath Comments: bubl@bubl.ac.uk Finite Mathematics and Applied Calculus Resource Page Set of book extracts, topic summaries, tutorials, online texts, quizzes, review exercises and software utilities in the area of finite mathematics and applied calculus. Author: Subjects: calculus, mathematics education, trigonometry DeweyClass: Resource type: guide Introduction to Trigonometry An introductory guide to trigonometry. Includes functions, inverse functions and equations. Author: Claeys, Johan Subjects: trigonometry DeweyClass: Resource type: guide Mathematics Archives Mathematics resources covering a range of topics including algebra, geometry, fractals, numerical analysis, statistics and trigonometry. Materials include bibliographies, images, photographs, problems, proofs, theories, conference proceedings and teaching materials. In addition to traditional subjects, the application of maths in art and music is considered and mathematics software is reviewed. Author: Mathematics Archives Subjects: algebra, fractals, geometry, mathematics education, mathematics software, numerical analysis, trigonometry

76. Information Of Products Information of Products Sine Function Box Cosine Function Box Tangent Function Box The graph of y=sin x The graph of y=cos x Graph of y=sin ax http://www.ies.co.jp/math/java/trig/index.html

Information of Products Information of Products

77. Trigonometric Functions The use of trigonometric functions arises from the early connection between mathematics and astronomy. Early work with spherical triangles was as important 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.

78. HyperMath Hyperbolic functions Index HyperPhysics****HyperMath Go Back. http://hyperphysics.phy-astr.gsu.edu/hbase/trig.html

Hyperbolic functions Index HyperPhysics HyperMath Hyperbolic functions Index HyperPhysics HyperMath ... Go Back

79. Trigonometric Functions This chapter explains how the trig functions of sin, cos, tan, csc, sec and cot can be used to solve porblems. http://www.intmath.com/Trigonometric-functions/Trig-functions-intro.php

This is interactive mathematics where you learn math by playing with it! home sitemap LiveMath info Flash highlights ... feedback Trigonometric Functions by M. Bourne Why learn about trigonometric functions...? The trigonometric functions are very important in technical subjects like science, engineering, architecture, and even medicine. You will come across trig functions all the time and you are encouraged to learn them well! Example problem: The top of the Sydney Opera House is about 67 m above sea level. Have you ever thought about how to measure the height? See how this is done in The Right Triangle and its Applications Surveying is one of the many applications. Road makers, bridge builders and those whose job it is to get buildings in the right place all use trigonometry in their daily work. For more applications and examples of trigonometry in Interactive Mathematics, check out the many Uses of Trigonometry In this chapter we start by explaining the basic trigonometric functions using degrees radians and how they are used in trigonometry. In this Chapter Related Sections in "Interactive Mathematics"

80. Trigonometric Indentities Trigonometric Identities. sin(theta) = a / c. csc(theta) = 1 / sin(theta) = c / a. cos(theta) = b / c. sec(theta) = 1 / cos(theta) = c / b http://math2.org/math/trig/identities.htm

Trigonometric Identities sin(theta) = a / c csc(theta) = 1 / sin(theta) = c / a cos(theta) = b / c sec(theta) = 1 / cos(theta) = c / b tan(theta) = sin(theta) / cos(theta) = a / b cot(theta) = 1/ tan(theta) = b / a sin(-x) = -sin(x) csc(-x) = -csc(x) cos(-x) = cos(x) sec(-x) = sec(x) tan(-x) = -tan(x) cot(-x) = -cot(x) sin (x) + cos (x) = 1 tan (x) + 1 = sec (x) cot (x) + 1 = csc (x) sin(x y) = sin x cos y cos x sin y cos(x y) = cos x cosy sin x sin y tan(x y) = (tan x tan y) / (1 tan x tan y) sin(2x) = 2 sin x cos x cos(2x) = cos (x) - sin (x) = 2 cos (x) - 1 = 1 - 2 sin (x) tan(2x) = 2 tan(x) / (1 - tan (x)) sin (x) = 1/2 - 1/2 cos(2x) cos (x) = 1/2 + 1/2 cos(2x) sin x - sin y = 2 sin( (x - y)/2 ) cos( (x + y)/2 ) cos x - cos y = -2 sin( (x-y)/2 ) sin( (x + y)/2 ) Trig Table of Common Angles angle sin (a) cos (a) tan (a) Given Triangle abc, with angles A,B,C; a is opposite to A, b oppositite B, c opposite C: a/sin(A) = b/sin(B) = c/sin(C) (Law of Sines) c = a + b - 2ab cos(C) b = a + c - 2ac cos(B) a = b + c - 2bc cos(A) (Law of Cosines) (a - b)/(a + b) = tan 1/2(A-B) / tan 1/2(A+B) (Law of Tangents)

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