1. ThinkQuest : Library : Seeing Is Believing A brief overview of trigonometric terms and concepts. http://library.thinkquest.org/10030/trigcon.htm

Index Education Seeing is Believing Need a primer on math, science, technology, education, or art, or just looking for a new Internet search engine? This catch-all site covers them all. Maybe you're doing your homework and need to quickly look up a basic term? Here you'll find a brief yet concise reference source for all these topics. And if you're still not sure what's here, use the search feature to scan the entire site for your topic. Visit Site 1997 ThinkQuest Internet Challenge Languages English Students Peter Oakhill College, Castle Hill, Sydney, Australia Suranthe H Oakhill College, Sydney, Australia Coaches Tina Oakhill College, Castle Hill, Sydney, Australia Tina Oakhill College, Castle Hill, Sydney, Australia Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

2. Dave's Short Course In Trigonometry Applications of trigonometry Astronomy and geography; Engineering and physics; Mathematics and its applications. What is trigonometry? http://aleph0.clarku.edu/~djoyce/java/trig/

Dave's Short Trig Course Table of Contents Who should take this course? Trigonometry for you Your background How to learn trigonometry Applications of trigonometry Astronomy and geography Engineering and physics Mathematics and its applications What is trigonometry? Trigonometry as computational geometry Angle measurement and tables Background on geometry The Pythagorean theorem An explanation of the Pythagorean theorem Similar triangles Angle measurement The concept of angle Radians and arc length Exercises, hints, and answers About digits of accuracy Chords What is a chord? Trigonometry began with chords Sines The relation between sines and chords The word "sine" Sines and right triangles The standard notation for a right triangle Exercises, hints, and answers Cosines Definition of cosine Right triangles and cosines The Pythagorean identity for sines and cosines Sines and cosines for special common angles Exercises, hints, and answers Tangents and slope The definition of the tangent Tangent in terms of sine and cosine Tangents and right triangles Slopes of lines Angles of elevation and depression Common angles again Exercises, hints, and answers

3. Trigonometry A trigonometry tutorial which aims to communicate the point of trigonometry, as well as the basics of the discipline. What is trigonometry? trigonometry is the branch of mathematics that deals with triangles, circles, oscillations work, on some level; so trigonometry turns out to be fundamental to http://fergusmurray.members.beeb.net/trig.htm

What is Trigonometry? Trigonometry is the branch of mathematics that deals with triangle s, circle s, oscillation s and waves ; it is absolutely crucial to much of geometry and physics . You'll often hear it described as if it was all about triangles, but I think that is missing much of the point. Waves and resonance are at the root of how matter works at the most fundamental level ; they are behind how sound and light move, and probably also how mind s and beauty work, on some level; so trigonometry turns out to be fundamental to pretty much everything. Any time you want to figure out anything to do with angle s, or turning, or swinging , there's trigonometry involved. The first thing to understand with trigonometry is why the mathematics of right-angled triangles should also be the mathematics of circles. Picture a line which can turn around one of its ends, like the hand of a clock . Obviously, the moving end of the line traces out a circle - it's like drawing with a

4. Trigonometry trigonometry. A listing of material is given below. Other tutorial materials in English and Maths are available at www.mimesis.net. Introduction. Radian Measure. Trig. ratios for acute angles. Trig . http://www.acts.tinet.ie/trigonometry_645.html

Prev Next Home ] Created 7/7/96 by jevans@tinet.ie Trigonometry A listing of material is given below. Other tutorial materials in English and Maths are available at www.mimesis.net Introduction Radian Measure Trig. ratios for acute angles ... Trigonometry of the triangle -Surface Links- Core Resources by Topic - Core and Options LC - Higher Level Leaving Certificate Mathematics ... Home

5. Trigonometry : Trigonometric Functions & Identities In Math Three comprehensive modules from Syvum. Each includes theory and explanation, along with practice exercises. http://www.syvum.com/math/trigonometry.html

Syvum Home K-12 GMAT GRE ... More... '); document.writeln(' '); document.writeln(' Trigonometry Table of Contents Title Trigonometry Module 1: Trigonometric Functions Sin, Cos and Tan Functions Cosec, Sec and Cot Functions Practice Exercise for Trigonometry Module 1: Trigonometric Functions ... Practice Exercise for Trigonometry Module 3: Word Problems on Heights and Distances $$$ WIN $$$ PRIZES Enter Syvum Quizenius CONTEST NOW ! fiSearchFormMaxSetId='AX005650'; Suppress Pop-ups Online Translation - Dictionary One-Click Lookups Contact Info

6. Mathematics Archives - Topics In Mathematics - Trigonometry trigonometry. Complex Numbers and trigonometry. ADD. KEYWORDS Tutorial, Angles and KEYWORDS Important trigonometry Identities, trigonometry Review, trigonometry Word Problems http://archives.math.utk.edu/topics/trigonometry.html

Topics in Mathematics Trigonometry Complex Numbers and Trigonometry ADD. KEYWORDS: Tutorial, Angles and Triangles, Similar Triangles, Parallelograms, Polar Form, Negative of a Point, Subtraction, Conjugate, The Real and Imaginary Axes; Rectangular Form, Trigonometric Functions, Inverse Trigonometric Functions, Laws of Sines and Cosines SOURCE: Abraham P. Hillman, University Of New Mexico, Gerald L. Alexanderson, Santa Clara University and Mervin E. Newton, Thiel College TECHNOLOGY: PDF reader Easymaths ADD. KEYWORDS: Tutorials, Worksheets, Diagnostic tests SOURCE: Mathematics Web Association EMR - Exercises in Math Readiness ADD. KEYWORDS: Tutorial, Radian Measure, Trig Identities Frequently Asked Questions About Trigonometry ADD. KEYWORDS: Tutorial GCSE Mathematics ADD. KEYWORDS: Tutorial, Drill problems, Negative Numbers, Ratios, Fractions, Graphs, Probability, Algebra, Trigonometry, Functions and Sequences Geomath - Trigonometry ADD. KEYWORDS: Tutorial How to estimate Saturn's Mass and Distance The Interactive Learning Network - Trigonometry ADD. KEYWORDS:

7. S.O.S. Math - Trigonometry Copyright Disclaimer Privacy Concerns? trigonometry Angle Measures; Trigonometric Functions The magic identity; The Addition Formulas; 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

8. Math.com Homework Help Trigonometry Free math lessons and math homework help from basic math to algebra, geometry and beyond. Students, teachers, parents, and everyone can find solutions to their math problems instantly. Search. More trigonometry coming soon! Be sure to check out our special CD trigonometry offer below. http://www.math.com/homeworkhelp/Trigonometry.html

Home Teacher Parents Glossary ... Email this page to a friend Select Subject -Select Subject Basic Math Everyday Math Pre-Algebra Algebra Geometry Trigonometry Statistics Calculus Advanced Topics Others Resources Cool Tools References Test Preparation Study Tips ... Wonders of Math Search More Trigonometry coming soon! Be sure to check out our special CD Trigonometry offer below. Calculators Functions Overview The functions Unit modes - degree, radian, grad ... Legal Notices . Please read our Privacy Policy

9. An Introduction To TRIGONOMETRY An introduction to trigonometry. Turning counterclockwise is the positive orientation in trigonometry. Angles are measured starting from the xaxis. http://www.ping.be/~ping1339/gonio.htm

An introduction to TRIGONOMETRY Definitions and basics Trigonometric circle and angles Trigonometric numbers of a real number t Basic formulas ... Calculations with inverse trigonometric functions Definitions and basics Trigonometric circle and angles Take an x-axis and an y-axis (orthonormal) and let O be the origin. A circle centered in O and with radius = 1, is called a trigonometric circle or unit circle. Turning counterclockwise is the positive orientation in trigonometry. Angles are measured starting from the x-axis. Two units to measure an angle are degrees and radians An orthogonal angle = 90 degrees = pi/2 radians In this theory we use mainly radians. With each real number t corresponds just one angle, and just one point P on the unit circle, when we start measuring on the x-axis. We call that point the image point of t. Examples: with pi/6 corresponds the angle t and point P on the circle. with -pi/2 corresponds the angle u and point Q on the circle. Trigonometric numbers of a real number t With t radians corresponds exactly one point p on the unit circle.

10. Trigonometry Worksheets! Welcome to our trigonometry worksheet section. Comments? Every time you click to create a worksheet a New worksheet is created! trigonometry. Radian Measure. Arc Length. Coordinate System. Trigonometric Functions on a General Angle http://www.edhelper.com/trigonometry.htm

Return to edHelper.com Welcome to our trigonometry worksheet section. Comments? Every time you click to create a worksheet a New worksheet is created! Trigonometry Radian Measure Arc Length Coordinate System Trigonometric Functions on a General Angle ... Back to the Math Table Of Contents Radian Measure A radian is a unit of angle measure. The radian measure of a central angle of a circle compares the length of its intercepted arc with the length of the radius of the circle. One radian is the measure of a central angle of a circle that intercepts an arc whose length equals the radius of the circle. Given a central angle q in radians, s represents the length of its intercepted arc, with radius r: q s r or s = r q To change from degrees to radians: Multiple the number of degrees by To change from radians to degrees: Multiple the number of radians by Build Worksheet Arc Length Use the s = r q equation to solve these word problems. Example: The minute hand of a clock is 12 cm long. How far does the tip of the hand move in 10 minutes? To use the s = r q equation, first convert 60

11. Basic Trigonometry BASIC trigonometry. THE RIGHT TRIANGLE. For a triangle to be called a right triangle, one of the interior angles must be 90 degrees. http://abe.www.ecn.purdue.edu/~agen215/trig.html

BASIC TRIGONOMETRY THE RIGHT TRIANGLE For a triangle to be called a right triangle , one of the interior angles must be 90 degrees. The sum of the interior angles must be 180 degrees , as with all triangles. TRIGONOMETRIC FUNCTIONS PYTHAGOREAN THEOREM Given the length of the side opposite and the side adjacent of a right triangle, the hypotenuse can be calculated by the following formula: You can actually find any third side of a triangle, if the other two sides are known. SUM OF INTERIOR ANGLES If "n" is the number of vertices (corners) of a closed shape, the sum of the interior angles can be found by: What is the sum of the interior angles for the fourth shape above? Because it has four vertices, (4-2) * 180 = 360 degrees, like any four-sided shape. GRADE AND PERCENT GRADE To calculate the grade, use the following formula: For this example, the grade equals (25/500) = 0.05 The percent grade equals (25/500) * 100 = 5% CONVERTING MAP AREA TO FIELD AREA If you are dealing with an area, in which the unit is square feet, or some such unit, you must square the scale of the map to calculate the proper area. Field Area = Map Area * (Map Scale)^2 So if the map has a scale of 1 in. = 2000 ft., and you measure a field to have a map area of 7.0 square inches, the total area is:

12. Dave's Short Trig Course Dave's short trig course This World Wide Web (WWW) site introduces trigonometry as computational geometry and offers explanations and illustrations of basic trigonometry concepts. The site, with http://rdre1.inktomi.com/click?u=http://aleph0.clarku.edu/%7Edjoyce/java/trig/in

13. Applications Of Trigonometry Applications of trigonometry. What can you do with trig? The kind of trigonometry needed to understand positions on a sphere is called spherical trigonometry. http://aleph0.clarku.edu/~djoyce/java/trig/apps.html

Applications of trigonometry What can you do with trig? Historically, it was developed for astronomy and geography, but scientists have been using it for centuries for other purposes, too. Besides other fields of mathematics, trig is used in physics, engineering, and chemistry. Within mathematics, trig is used in primarily in calculus (which is perhaps its greatest application), linear algebra, and statistics. Since these fields are used throughout the natural and social sciences, trig is a very useful subject to know. Astronomy and geography Trigonometric tables were created over two thousand years ago for computations in astronomy. The stars were thought to be fixed on a crystal sphere of great size, and that model was perfect for practical purposes. Only the planets (Mercury, Venus, Mars, Jupiter, Saturn, the moon, and the sun) moved on the sphere. The kind of trigonometry needed to understand positions on a sphere is called spherical trigonometry. Spherical trigonometry is rarely taught now since its job has been taken over by linear algebra. Nonetheless, one application of trigonometry is astronomy. As the earth is also a sphere, trigonometry is used in geography and in navigation. Ptolemy (100-178) used trigonometry in his

14. Mathematics, Mental Math & Calculation; Tutorials On Fuzzy Logic And Sets, Neura Exercise tool to practice addition, subtraction, multiplication, division, trigonometry and fuzzy logic problems. http://www.answermath.com/

answermath HOME New Loan Calculator answermath en Español answermath in Italiano Practice on line: Addition Subtraction Multiplication Division ... Tangent Practice on line: Try to do it in your head...Select a level...Write your Answer by clicking the pad... ...We'll tell how you did and see how fast you did it... Mental Math Tips and Tricks: Ways to help you solve mathematical operations easily in your head... Artificial Intelligence Tutorials: Data Mining Neural Networks Fuzzy Logic Fuzzy Control Lab. ... Campos, Vectores y Sistemas De Coordenadas Artificial Intelligence Tutorials: Neural Networks, Fuzzy Logic and Sets, and Data Mining...Fuzzy Control Lab. and Artificial Life Lab... Campos y Vectores Sistemas de Coordenadas: Rectangulares, Cilíndricas y Esféricas Operadores: Gradiente, Divergencia, Rotacional y Laplaciano iPowerWeb - Introducing the most powerful hosting solution Home Site Map Suggest a link ... Help

15. S.O.S. Mathematics - Trigonometry S.O.S. Mathematics trigonometry The trigonometry index of S.O.S. Math features a table of trigonometric identities, lessons on functions and formulae, and a section of exercises and solutions. http://rdre1.inktomi.com/click?u=http://www.sosmath.com/trig/trig.html&y=027

16. Angle Measures trigonometry MEASURE OF AN ANGLE. Any real number may be interpreted as the radian measure of an angle as follows If , think of http://www.sosmath.com/trig/Trig1/trig1/trig1.html

TRIGONOMETRY - MEASURE OF AN ANGLE Any real number may be interpreted as the radian measure of an angle as follows: If , think of wrapping a length of string around the standard unit circle C in the plane, with initial point P (1,0), and proceeding counterclockwise around the circle; do the same if , but wrap the string clockwise around the circle. This process is described in Figure 1 below. Figure 1 If Q x y ) is the point on the circle where the string ends, we may think of as being an angle by associating to it the central angle with vertex O (0,0) and sides passing through the points P and Q . If instead of wrapping a length s of string around the unit circle, we decide to wrap it around a circle of radius R , the angle (in radians) generated in the process will satisfy the following relation: Observe that the length s of string gives the measure of the angle only when R As a matter of common practice and convenience, it is useful to measure angles in degrees , which are defined by partitioning one whole revolution into 360 equal parts, each of which is then called one degree. In this way, one whole revolution around the unit circle measures radians and also 360 degrees (or ), that is:

17. 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/

A complete course in arithmetic: Add, subtract, multiply, divide. Mental arithmetic Powers of 10 Regrouping Decimals Parts of natural numbers Fractions Percent Trigonometry from the very beginning: Ratio and proportion Definitions of the trigonometric functions Solve right triangles The 30-60-90 triangle The law of sines The law of cosines The unit circle Radian measure Arc length The formal rules of algebra Rational and irrational numbers Functions and graphs Logarithms The binomial theorem Mathematical induction The ratio of natural numbers Measurement: Geometry and arithmetic Common measure Incommensurable magnitudes Irrational numbers

18. Arc Distance Formula By James Q. Jacobs Finding the shortest distance between two points on the earth given latitude and longitude. Download ARC_CALC_3, Microsoft Excel version, A Spherical Triangle Calculator by James Q. Jacobs. http://www.jqjacobs.net/astro/arc_form.html

Spherical Trigonometry Arc Distance Formula Finding the shortest distance between two points on the earth given latitude and longitude. Spherical Triangle Calculator Download ARC_CALC_3 . This small program will do the calculations below in an Excel 4.0 spreadsheet. You only need to input the coordinates. The program supports input of three sites and calculates the three arc distances, the area of the spherical triangle and the bearings between sites. Most spreadsheet programs should be able to import this file format. The graphic below illustrates the spreadsheet, before corrections on July 24, 2002. Previous downloads have "A to C" and "B to C" labels swapped for arcs and bearings. Let me know if there are other bugs in the applet. Epoch_2000 Temporal Epoch Calculator is a similar Excel spreadsheet. It calculates the temporal changes in astronomic constants, obliquity of the ecliptic and illumination angles at any specified latitude. You just enter the latitude and the date. Sherical Trigonometry Arc Distance Formulas Note: a and b are distinct from a (alpha) and b (beta).

19. Frequently Asked Questions About Trigonometry Frequently asked questions about trigonometry This World Wide Web (WWW) site offers trigonometry students an interactive format for investigating introductory concepts involving sine, cosine, and http://rdre1.inktomi.com/click?u=http://catcode.com/trig/index.html&y=02045A

20. Problems About Trigonometry Problems about trigonometry. read the solution. Problems about trigonometry. Level 1 problems. Calculate cos(3u) in terms of cos(u). http://www.ping.be/~ping1339/Pgonio.htm

Problems about trigonometry READ THIS FIRST Problems about trigonometry Level 1 problems Level 2 problems ... Level 3 problems READ THIS FIRST If a problem is solved. It is not 'the' answer. No attempt is made to search for the most elegant answer. I highly recommend that you at least try to solve the problem before you read the solution. Problems about trigonometry Level 1 problems Calculate cos(3u) in terms of cos(u) cos(2u+u) = cos(2u)cos(u)-sin(2u)sin(u) = (cos (u)-sin (u))cos(u)-2sin(u)cos(u)sin(u) = cos (u) - sin (u)cos(u)-2sin (u)cos(u) = cos (u) -3sin (u)cos(u) cos (u) -3cos(u)+3cos (u) 4cos (u) -3cos(u) In the same way sin(3u) = -4sin (u) -3sin(u) prove that : cos(t)+sin(t) cos(2t) - = - cos(t)-sin(t) 1- sin(2t) cos(2t) = 1- sin(2t) cos (t)-sin (t) (cos(t)-sin(t))(cos(t)+sin(t)) - = = 1-2sin(t)cos(t) cos(t)cos(t)-2sin(t)cos(t)+sin(t)sin(t) (cos(t)-sin(t))(cos(t)+sin(t)) - = (cos(t)-sin(t))(cos(t)-sin(t)) cos(t)+sin(t) cos(t)-sin(t) show that sin(p)-sin(q) p+q = cot(-) cos(q)-cos(p) 2 sin(p)-sin(q) = cos(q)-cos(p) 2cos((p+q)/2)sin((p-q)/2) = -2sin((p+q)/2)sin((q-p)/2) cos((p+q)/2) = sin((p+q)/2) p+q cot(-) 2 Solve (sin(2a)).x

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