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CoreConcepts

Trigonometry

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Vectors

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Junior High
High School
College
10/30/99 - http://www.maths.lancs.ac.uk/~gilbert/m102a/node2.html
Line Segments and Position Vectors - Simple definition of vectors and real world usage.
Junior High
High School
College
10/20/99 - http://www.brookscole.com/engineering/math/modules/
topics/precalc/trig/learn.htm
- Right Triangle Applications of the Trigonometric Functions - Given at least one side and one other side or angle of a right triangle, the other six sides and angles can be determined using the trigonometric functions. Also contains info on vectors and graphs of trig functions.
Junior High
High School
College
10/25/99 - http://library.advanced.org/10030/4vectors.htm
Vectors - A vector is a quantity that has both direction and magnitude. A vector is denoted by a directed line segment. The magnitude of a vector is the length of the segment and the direction of a vector is where the segment is pointing.
Junior High
High School
College
11/6/99 - http://www.netcomuk.co.uk/~jenolive/homevec.html
Working with Vectors - This is a very good page that has a list of basic through complex vector discussions. Use the index to go to the places you need help with.
Junior High
High School
College
11/5/99 - http://www.physics.uoguelph.ca/tutorials/vectors/vectors.html
Vectors - This page is very informative to the ideas of vectors. Also contains info on the polar coordinate system.

Trigonometry of Triangles

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Junior High
High School
College
10/25/99 - http://library.advanced.org/10030/3thearea.htm
The Area Of A Triangle - The formula for finding the area of oblique triangles.
Junior High
High School
College
10/30/99 - http://www.sisweb.com/math/trig/tables.htm
Trigonometric Tables - Contains a complete table for all angles and also a common angle table.
Junior High
High School
College
11/5/99 - http://id.mind.net/~zona/mmts/trigonometryRealms/introduction/
rightTriangle/trigRightTriangle.html
- Trigonometry and Right Triangles - Excellent page explaining the theory of solving right triangles. Includes good pictures and applets for easy understanding.
Junior High
High School
College
10/20/99 - http://aleph0.clarku.edu/~djoyce/java/trig/oblique.html
Oblique Triangles - An oblique triangle is any triangle that is not a right triangle. It could be an acute triangle (all three angles of the triangle are less than right angles) or it could be an obtuse triangle (one of the three angles is greater than a right angle). Actual
Junior High
High School
College
11/1/99 - http://www.sci.wsu.edu/math/Review/107/trigBasics.html
Trig Bas - Contains the general trig functions and table and graph to help you get started.
Junior High
High School
College
11/5/99 - http://www.gcse.com/Maths/teach/trig1.htm
Mathematics Tutorial in Trig 1 - This page is the start of a well laid out tutorial. It has a step by step progression in solving right triangles and the laws of sine and cosine
Junior High
High School
College
11/5/99 - http://www.gcse.com/Maths/Easy/w1.htm
Mathematics Tutorial in Trig 2 - This page is a very good tutorial on the general triangle and solving those triangles. Step by step progression with some problems available to increase understanding.
Junior High
High School
College
11/5/99 - http://www.acts.tinet.ie/trigonometryofthetrian_673.html
Trigonometry of the Triangle - Contains general inormation on the trigonometry of triangles. Sine rule, Cosine rule, Area of a triangle, and Small angles are included here.

Graphs of Trigonometric Functions

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Junior High
High School
College
10/28/99 - http://www.sisweb.com/math/graphs/trig.htm
Dave’s Trig Graphs - Shows the basic trig graphs.
Junior High
High School
College
10/20/99 - http://aleph0.clarku.edu/~djoyce/java/trig/functions.html
Trigonometric Functions - We've used the unit circle to define the trigonometric functions for acute angles so far. We'll need more than acute angles in the next section where we'll look at oblique triangles. Some oblique triangles are obtuse and we'll need to know the sine and co
Junior High
High School
College
10/20/99 - http://math.usask.ca/readin/mwtf.html
Modeling with Trig. Functions - After completing the previous sections on Trigonometric Functions, we are almost ready to try and work on "real world" problems. But before getting to that uses sine graph to help solve real world type problems.
Junior High
High School
College
10/24/99 - http://www.npac.syr.edu/REU/reu94/williams/ch1/subsection3_4_6.html
Trig Function Graphs - Shows the six trigonometric function graphs.
Junior High
High School
College
11/1/99 - http://www.sci.wsu.edu/math/Review/107/trigGraphs.html
Trig Graps - General forms of a sine function and the ways to properly graph the functions in trig.
Junior High
High School
College
11/5/99 - http://www.math.uga.edu/~john/Graphs_Other_Trig_Functions.ppt
Graphs of other trig functions - Contains graphs of the more complex trig functions. This site is arranged as a slide show and is easy to navigate.

Trigonometric Functions

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Junior High
High School
College
10/20/99 - http://aleph0.clarku.edu/~djoyce/java/trig/angle.html
Angle measurement - The concept of angle is one of the most important concepts in geometry. The concepts of equality, sums, and differences of angles are important and used throughout geometry, but the subject of trigonometry is based on the measurement of angles
Junior High
High School
College
10/20/99 - http://www.sosmath.com/trig/Trig1/trig1/trig1.html
Measure of an angle - Shows how to measure angles and the common systems of measurement. Contains graphs and sample problems.
Junior High
High School
College
10/20/99 - http://math.usask.ca/readin/rmoa.html
Radian Measure of Angles - If a unit circle is drawn with the vertex of an angle at its center, then the measure of this angle in RADIANS is the length of the arc that subtends the angle.
Junior High
High School
College
10/20/99 - http://math.usask.ca/readin/trfn.html
Trigonometric Functions - One of the easier ways to start understanding trigonometric functions is by picturing a right triangle. This will allow the concept to be understood.
Junior High
High School
College
10/20/99 - http://math.usask.ca/readin/motf.html
More Trigonometric Functions - We know that there are special reference angles in the unit circle that come up in many of the calculations. Here is a quick reference of the trig values of these angles.

Trigonometric Identities

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Junior High
High School
College
10/20/99 - http://aleph0.clarku.edu/~djoyce/java/trig/identities.html
Summary of trigonometric identities - You have seen quite a few trigonometric identities in the past few pages. It is convenient to have a summary of them for reference. This page lists the identities and organizes them based on usage.
Junior High
High School
College
10/20/99 - http://www.sosmath.com/trig/Trig5/trig5/trig5.html
Table of Trigonometric Functions - This page lays out all the different trig identities you’ll use in trig. Contains fundamental, addition, double-angle, half-angle, product-to-sum, and sum-to-product identities.
Junior High
High School
College
10/20/99 - http://www.sosmath.com/trig/magicide/magicide.html
The Magic Identity - Trigonometry is the art of doing algebra over the circle. So it is a mixture of algebra and geometry. The sine and cosine functions are just the coordinates of a point on the unit circle. This implies the most fundamental formula in trigonometry (which we
Junior High
High School
College
10/20/99 - http://www.sosmath.com/trig/addform/addform.html
The Addition Formulas - The fundmental identities are very important for the analysis of trigonometric expressions and functions but they are a direct result of the intimate relation between trigonometry and geometry. The power behind the algebraic nature of trigonometry is hidd
Junior High
High School
College
10/20/99 - http://www.sosmath.com/trig/douangl/douangl.html
Double and Half Angle Formulas - Double-Angle and Half-Angle formulas are very useful. For example, rational functions of sine and cosine would be very hard to integrate without these formulas. They are discussed in detail.
Junior High
High School
College
10/20/99 - http://www.sosmath.com/trig/prodform/prodform.html
Product and Sum Formulas - From the Addition Formulas, we deive the following trigonometric formulas of Product and Sum Formulas
Junior High
High School
College
10/20/99 - http://math.usask.ca/readin/trid.html
Trig. Identities - Trigonometric functions are all related to each other through different equations. These are called the TRIGONOMETRIC IDENTITIES and are covered on this page.

Polar Coordinates and Complex Numbers

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Junior High
High School
College
10/25/99 - http://library.advanced.org/10030/5polar.htm
Polar Coordinates - The origin or pole of polar coordinates called point O and a horizontal half line with the endpoint O, called the polar axis, is a nonnegative line which the length of a segment can be measured. Angle q is the angle in which the terminal side is rotated.
Junior High
High School
College
10/25/99 - http://library.advanced.org/10030/5conver.htm
Converting Coordinate Systems - Shows the relationships and how to convert coordinates to polar coordinates.
Junior High
High School
College
10/25/99 - http://library.advanced.org/10030/6trigon.htm
Trig Form Of Complex Numbers - Contains info on the geometry of complex numbers and their relations to trigonometry.
Junior High
High School
College
11/5/99 - http://www.ping.be/math/polar.htm#Polar-coordinates-of
Polar Coordinates - This site is very thorough in its discussion of polar coordinates and the polar coordinate system. Includes polar to Cartesian conversions and much more
Junior High
High School
College
11/5/99 - http://www.geom.umn.edu/docs/reference/CRC-formulas/node5.html#SECTION01130000000000000000
Polar Coordinates in the Plane - This page is great to start off on when studying polar coordinates. It entails the polar coordinate system and the conversion between polar and Cartesian coordinates.

Inverse Functions and Equations

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Junior High
High School
College
10/20/99 - http://aleph0.clarku.edu/~djoyce/java/trig/right.html
Right Triangles - We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. We can use these properties and find the inverse trig functions and use those to solve triang
Junior High
High School
College
11/1/99 - http://www.acts.tinet.ie/inversetrig.functions_668.html
Inverse trig functions - Contains graphs and tables on the inverse trig functions.
Junior High
High School
College
11/1/99 - http://www.gnu.org/manual/glibc-2.0.6/html_node/libc_256.html#SEC256
Inverse trig functions - Defines the trig functions as used on a calculator.
Junior High
High School
College
11/1/99 - http://www.sci.wsu.edu/math/Review/107/inverses.html
Inverse trig functions - Shows the student the steps to find the inverse of a trig function.
Junior High
High School
College
11/5/99 - http://www.math.uga.edu/~john/Inverse_Trig_Fctns_I.ppt
Inverse Trig Functions - This site contains the basics of inverse trig functions. It is laid out in the form of a slide show.

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