21. Trigonometry Start The trigonometry Explorer is a highly interactive multimedia explorationof trigonometry fundamentals. THE trigonometry EXPLORER ONLINE. http://www.cogtech.com/EXPLORER/Start.htm

THE TRIGONOMETRY EXPLORER ON-LINE Click on the icons to the left to to view small Shockwave portions of the CD-ROM. Click on linked words on the left to go to other related resources. Cognitive Technologies Corporation's (CTC) goal is to provide a quality educational site that includes math, science, literature, social studies, and the arts serving students ages 8 to 18. We employ interactive tutoring, animation, fun real world applications and exploration activities to teach and motivate. The CD-ROM contains over 300 Megabytes of lessons, applications, and problems. It uses voice, music, and creative animations, and many interactive activity. To order call 1-800-335-0781 Click here for a complete outline of the CD-ROM's content. Click here for CD-ROM Customer Support Requirements, Price and Ordering Minimum System Requirements: PC: Windows (3.1 or 95), 486/25 processor, 8 Meg RAM, 2x CD-ROM Drive, sound recommended. MAC: System 7.1 or higher, 040 processor, 8 Meg RAM, 2x CD-ROM Drive, sound recommended. Home Versions Procuct ID# Product Description Unit Price The Trigonometry Explorer-Home School Versions School Version with Teacher's Manual The teacher's manual includes many additional problems the teacher may copy and distribute to students. Provides discussion questions on the lessons and the real world applications. Provides further discussion of the applications to deepen the teacher's understanding. Provides helpful teacher tips to students on what to look for as they navigate through the program.

22. Basic Trigonometry Cosine, sine and tangent are defined. The Pythagorean thereom is illustrated as well the number of Category Kids and Teens School Time Math trigonometry......BASIC trigonometry. THE RIGHT TRIANGLE. For a triangle to be calleda 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:

23. The Math Forum Trig/Calc Problem Of The Week This is the trigonometry and Calculus weekly interactive math project. AMath Forum Project. trigonometry and Calculus Problem of the Week. http://mathforum.org/calcpow/

A Math Forum Project Trigonometry and Calculus Problem of the Week Student Center Teachers' Place All Problems of the Week Search Calcpows ... Problem of the Week Library Sorry, no puzzles are currently available Math Forum Home Math Library Quick Reference Math Forum Search ... calcpow@mathforum.org

24. Math Forum - Ask Dr. Math Archives: High School Trigonometry Browse High School trigonometry. Basics of trigonometry 12/12/2001Why is trigonometry important? How is it used in the real world? http://mathforum.org/library/drmath/sets/high_trigonometry.html

Ask Dr. Math High School Archive Dr. Math Home Elementary Middle School High School ... Dr. Math FAQ TOPICS This page: trigonometry Search Dr. Math See also the Dr. Math FAQ trigonometry formulas See also the Internet Library trigonometry HIGH SCHOOL About Math Analysis Algebra basic algebra ... Trigonometry Browse High School Trigonometry Stars indicate particularly interesting answers or good places to begin browsing. Averaging Two Angles How do you take the average of two or more angles? Basics of Trigonometry Why is trigonometry important? How is it used in the real world? Calculating Height in the Air I need to know the formula for calculating the height of an object, like how high in the air an object is. Carrying a Ladder around a Corner A ladder of length L is carried horizontally around a corner from a hall 3 feet wide into a hall 4 feet wide. What is the length of the ladder? Changing a Trigonometric Graph How do you graph: -cos 2x / 2? Curious Property of a Regular Heptagon How can I prove that in a regular heptagon ABCDEFG, (1/AB)=(1/AC)+(1/ AD)? Deriving Sines of 30, 45, 60 and 90 Degrees

25. Trigonometry Review trigonometry Review. Definitions of Trigonometric Functions. You need a Javaenabledbrowser 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

26. Trigonometry And Music trigonometry and Music. Sounds are produced by things that vibrate.Pure tones, like the the sounds produced by tuning forks, are 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.

27. Trigonometry - Maths Online Gallery trigonometry The applets are started by clicking the red buttons. Theapplet Triangle and Law of Sines emphasizes that the mathematical http://www.univie.ac.at/future.media/moe/galerie/trig/trig.html

Trigonometry The applets are started by clicking the red buttons. The applet Triangle and Law of Sines emphasizes that the mathematical symbols denoting lengths, angles and trigonometric functions in a triangle stand for concrete numbers. Furthermore, it illustrates (two versions of) the Law of Sines. Note that the applet does not provide a proof of the latter. For a multimedia proof see The Law of Sines by Math Education and Technology. The applet is started from the red button in its own window. Also see the learning units under Trigonometric functions Definition of the trig functions (applet) and under Functions 2 The graphs of sin, cos and tan (applet) Graphs of elementary trigonometric functions (graphics) Recognize functions 3 (puzzle, sine and cosine functions) Recognize graphs 3 (puzzle, sine and cosine functions) Gallery - Table of contents Maths links online tools topics ... Welcome Page

28. TCAEP.co.uk: Maths: Trigonometry Sponsored by the Institute of Physics Numbers Algebra trigonometry Calculus MatricesLimits Complex Numbers SI Units Symbols Printer Version, Maths trigonometry http://www.tcaep.co.uk/maths/trig/

Sponsored by the Institute of Physics Numbers Algebra Trigonometry ... Symbols Printer Version Maths Trigonometry Right-Angled Triangle Trigonometrical Identities Sine Law Cosine Law ... Tangent Law Click on an equation to see a larger version Right-Angled Triangle Right-angled triangle where a is the shortest side adjacent to angle b is the side opposite and c is the longest side (the hypotenuse) Trigonometrical Identities Sine Law Triangle where side a is opposite angle A , side b is opposite angle B and side c is opposite angle C Cosine Law Triangle where side a is opposite angle A , side b is opposite angle B and side c is opposite angle C Tangent Law Triangle where side a is opposite angle A , side b is opposite angle B and side c is opposite angle C H O M E S C I E N C E M A T H S A S T R O N O M Y ... About Page compiled: Wed Sep 05 18:37:57 GMT+01:00 2001

29. Math Help - Trigonometry Index - Technical Tutoring Provides detailed discussion of trigonometry concepts. Includes examples of varying difficulty.Category Kids and Teens School Time Math trigonometry...... Advanced Books · Speed Arithmetic · Math Index · Algebra Index · Trig Index· Chemistry Index · Gift Shop Technical Tutoring trigonometry Help Pages http://www.hyper-ad.com/tutoring/math/trig/

Technical Tutoring Home Site Index Advanced Books Speed Arithmetic ... Gift Shop Technical Tutoring Trigonometry Help Pages Index Review of Trigonometry Trigonometric Functions of Common Angles The Sine Function The Cosine Function ... Hyper-Ad Online Gift Shop New topics added regularly - Please come back! Last Modified: 02/18/01

30. Trigonometry trigonometry The very fast review. I. Basics. trigonometry is nothingmore than how to deal with angles versus straight lines. http://www.hyper-ad.com/tutoring/trig.htm

Basics Identities Examples Formulae · Exercizes · Advanced Keywords Navigation Recommended Books Site Index ... Gift Shop Trigonometry: The very fast review I. Basics Example The 45° triangle Figure 1- The 45° triangle According to Pythagorus, . Using the definitions of the trig functions gives us back to top Example 2. The 30°/60° triangle Figure 2 - The 30°/60° triangle According to Pythagorus, . Using the definitions of the trig functions gives back to top Example 3. The 15°/75° triangle Figure 3 - The 15°/75° triangle Now we make use of the formulas Addition , Subtraction There are other triangles, but I am lazy. Let's see how far you can get with just those I've done so far and a few simple laws (so you can add and subtract and multiply and divide angles). Please note that getting 1/3 of an angle is equivalent to trisecting it, a classic impossible problem! ( Advanced - because the answer depends on solving a cubic. The answer is rather dirty-looking, anyway). back to top And there are as many more as you care to memorize (always a mistake!). The hard part will be in coming up with smaller divisions (such as 5 degrees) without the arithmetic getting infinitely hairy. The author tried for hours and gave up! back to top II. Trig

31. 4 Trigonometry Review Next 4.1 Radians Up Ch.1 Review of Needed Previous 3.8 Compositionof Functions. 4 trigonometry Review. 4.1 Radians; 4.2 Conversion; http://www.npac.syr.edu/REU/reu94/williams/ch1/section3_4.html

Next: 4.1 Radians Up: Ch.1 Review of Needed Previous: 3.8 Composition of Functions 4 Trigonometry Review 4.1 Radians 4.2 Conversion 4.3 Trigonometric Functions 4.4 Sign (+ or -) of the Trig Functions ... 4.9.5 Half Angle mx_williams@smcvax.smcvt.edu

32. Multimedia Activities | Trigonometry Shockwave™ plugin required to view multimedia activities. trigonometry.Shifting and scaling sine and cosine curves Experiment http://www.exploremath.com/activities/activity_list.cfm?categoryID=6

33. Trigonometry And Astronomy http://www.geocities.com/Hollywood/Academy/8245/

34. Trigonometry Worksheets! Welcome to our trigonometry worksheet section. Comments? Every time you clickto create a worksheet a New worksheet is created! trigonometry 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

35. TheMathPage  Topics In Trigonometry 14. Functions of an Acute Angle. 15. trigonometry of Right Triangles. 16. The IsoscelesRight Triangle. Arc Length. 16. Analytic trigonometry The Unit. 16. Circle. http://www.themathpage.com/aTrig/trigonometry.htm

Home These pages are intended to be seen in Garamond THE TOPICS Ratio and Proportion Radicals: Rational and Irrational Numbers The Pythagorean Theorem ... Home Questions or comments? E-mail: Hello@themathpage.com . Please do not sent attachments.

36. Table Of Contents Trigonometry 4/e http://www.mathtv.com/Trig/pages/toc.htm

37. The U Of O Physics Student Page Vectors trigonometry. The following is a list of problems. To accessa problem, click on its title Converting from Polar to Cartesian http://zebu.uoregon.edu/~dmason/probs/bas/trig.html

The following is a list of problems. To access a problem, click on its title: Converting from Polar to Cartesian Coordinates Adding Vectors Hexagon Inscribed in a Circle The Earth Curving Away From You ... Surveying with a Protractor The U of O Physics Student Page last update: September 25, 1995 dmason@zebu.uoregon.edu

38. Math.com Homework Help Trigonometry Search, More trigonometry coming soon! Be sure to check out our special CD trigonometryoffer below. Tables Formulas, Calculators. Functions. ·, Overview. 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 ... Tangent FREE Software Click here to get your FREE Software Contact us Partnership Link to us Legal Notices . Please read our Privacy Policy

39. NAVIGATION AND TRIGONOMETRY The following is a short review of spherical trigonometry, celestial navigation,and great circle sailing. NAVIGATION trigonometry INDEX. http://www.angelfire.com/nt/navtrig/

INTRODUCTION AND INDEX - - The following is a short review of spherical trigonometry, celestial navigation, and great circle sailing. The solution of the navigation triangle (section C) can be used for great circle course determination and for determining a location of the observer from astronomical observations. There are many ways to solve spherical triangles, but my interest in this discussion are those methods that can be used on a calculator without the need of special tables. NAVIGATION TRIGONOMETRY INDEX The rhumb line, ( graphical Mercator sailing and middle latitude sailing ) Calculated Mercator sailing Definitions, the spherical triangle The right spherical triangle ... The oblique spherical triangle C1 The navigation triangle using the law of cosines C2 The navigation triangle using the Ageton method C3 The navigation triangle using Napiers analogies C4 The navigation triangle using the no-name method Approximation methods for great circle sailing Graphical great circle sailing Calculated great circle sailing ... Selected Navigation Stars EXTERNAL LINKS U. S. NAVAL OBSERVATORY

40. Trigonometry -- From MathWorld trigonometry, The study of angles and of the angular relationshipsof planar and threedimensional figures is known as trigonometry. http://mathworld.wolfram.com/Trigonometry.html

Geometry Trigonometry General Trigonometry Trigonometry The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular functions ) comprising trigonometry are the cosecant cosine cotangent secant ... sine , and tangent . The inverses of these functions are denoted , and . Note that the notation here means inverse function not f to the -1 power The trigonometric functions are most simply defined using the unit circle . Let be an angle measured counterclockwise from the x -axis along an arc of the circle . Then is the horizontal coordinate of the arc endpoint, and is the vertical component. The ratio is defined as . As a result of this definition, the trigonometric functions are periodic with period , so where n is an integer and func is a trigonometric function. A right triangle has three sides, which can be uniquely identified as the hypotenuse , adjacent to a given angle , or opposite . A helpful mnemonic for remembering the definitions of the trigonometric functions is then given by "oh, ah, oh-ah," From the Pythagorean theorem Therefore, it is also true that

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