Trigonometry - General problems & solutions

ARC LINKS: Tutorials and Web Resources for College Courses
This page contains a collection of hyperlinks to web resources in various college level subjects with an emphasis on math, science, engineering, and technology
Using the TI-83 Calculator
This tutorial is designed with the student in mind. The topics selected are those that students will use in college algebra, college trigonometry, and freshman calculus.
Trigonometric functions
Sin, Cos, Tan, Sec, Csc, Cot, Periodic Functions, Evaluation of Trigonometric functions
Trigonometric Functions
A TI-83 and a TI-84 have keys for three trigonometric functions: sine, cosine, and tangent. You will have to use a ratio to graph cosecant, secant, and cotangent.
TI-83/84 Plus Basic Math Programs (Trigonometry)
It also shows the area and perimeter and allows you to visualize the information graphically. This is the best Trigonometry Program ever seen on a TI-83.
Teacher Learning System
The Teacher Learning System for the TI-83 graphing calculator (TI-83 TLS) has been developed to assist the secondary mathematics teacher with learning about this technology
Free Trigonometry Tutorials and Problems
Free tutorials and problems on solving trigonometric equations, trigonometric identities and formulas can also be found
Dave's Short Trig Course
If you would like to learn a bit about trigonometry, or brush up on it, then read on. These notes are more of an introduction and guide than a full course.
Topics in Mathematics - Trigonometry
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
Trigonometry
During this tutorial you will be asked to perform calculations involving trigonometric functiions. You will need a calulator to proceed.
Trigonometry Tutorial
The classical concept of trigonometry deals with the relationships between the angles and sides of triangles.
Using the Graphing Calculator
graphing calculator tutorial, using the graphing calculator in secondary mathematics, Algebra, Geometry, Trigonomentry, PreCalclulus, Calculus
TI-83/84/89/92 Procedures and Help
This page points you to step-by-step procedures for several tasks on the TI-83; some procedures also show steps for the TI-89. (Keystrokes for all current models of TI-83 and TI-84 are nearly identical.
TI-83/83+/84+ Programs
Draw angles, calculate trig values. unitcirc.zip, Unit Circle/Trig Function Demonstration
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Trig General Probs
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Law of Sines
Trig Identities
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Trigonometric Functions

Trigonometric Functions
In this chapter we start by explaining the basic trigonometric functions using degrees (°), and in the later part of the chapter we will learn about radians and how they are used in trigonometry.
Trigonometric Functions
There are a few angles for which all trigonometric functions may be found using the triangles shown in the following
Webtrig
Trigonometry identities and functions
Trigonometric Functions
Arbitrary angles and the unit circle. 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.
Trigonometric Functions
One of the easier ways to start understanding trigonometric functions is by picturing a right triangle. (Refer back to the triangles section to recall this.) Let theta be one of the acute angles. Then we will label the triangle as follows:
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Trigonometric Equations

Solving Trigonometric Equations
This sections illustrates the process of solving trigonometric equations of various forms. It also shows you how to check your answer three different ways: algebraically, graphically, and using the concept of equivalence.
Solving Trigonometric Equations
A trigonometric equation is one that involves one or more of the six functions sine, cosine, tangent, cotangent, secant, and cosecant. Some trigonometric equations, like x = cos x, can be solved only numerically.
Using the Graphing Calculator in math - Table of Contents
MathBits.com is devoted to offering fun, yet challenging, lessons and activities in high school (and college level) mathematics and computer programming for students and teachers.
Trigonometric Equations
Using the table or graphs above and some algebra, solve the following equations for values between 0o and 360o.
Trigonometric equations - mathcentre
mathcentre has been established to deliver mathematics support materials, free of charge, to both university professionals and students.
Solving Trigonometric Equations
Let's look at two possible solution methods. The first method will work ONLY with Radians. The second method will work with Degrees and then convert back to Radians for the final answer.
TI-83/83+/84+ PROGRAMS
Henderson State University - math programs written for the TI-83/84 Calculator - Trigonometry/PreCalculus - College Algebra/PreCalculus
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Sine & Cosine

Sine-Cosine-Tangent
There are many complex parts to trigonometry and we aren't going there. We are going to limit ourselves to the very basics which are used in the study of airplanes.
Sine, Cosine, and Tangent
We can also find the measure of the angle ? when we know any of these three trigonometric ratios. Using a TI-83 calculator, we can determine what angle has this tangent.
Sine, Cosine and Tangent
Sine, Cosine and Tangent are all based on a Right-Angled Triangle. Before getting stuck into the functions, it helps to give a name to each side of a right triangle:
Sine, Cosine, and Tangent
In a right-angled triangle, the size of any angle is related to the ratio of the lengths of any two sides by the trigonometric functions. The basic functions are sine, cosine, and tangent.
 

Pythagorean Theorem

Pythagorean theorem
In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
Pythagorean Theorem
Many different proofs exist for this most fundamental of all geometric theorems. The theorem can also be generalized from a plane triangle to a trirectangular tetrahedron, in which case it is known as de Gua's theorem.
The Pythagorean Theorem
Proof #1: The simplest proof is an algebraic proof using similar triangles ABC, CBX, and ACX (in the diagram):
Pythagorean Theorem - Univerdity of Georgia
The Pythagorean Theorem was one of the earliest theorems known to ancient civilizations. This famous theorem is named for the Greek mathematician and philosopher, Pythagoras. Pythagoras founded the Pythagorean School of Mathematics in Cortona, a Greek seaport in Southern Italy.
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Trigonometry Law of Sines

Laws of Cosines and Sines
As usual, we'll use a standard notation for the angles and sides of a triangle. That means the side a is opposite the angle A, the side b is opposite the angle B, and the side c is opposite the angle C.
Solving Triangles
A triangle has six parts, three sides and three angles. Given almost any three of them — three sides, two sides and an angle, or one side and two angles — you can find the other three values. This is called solving the triangle, and you can do it with any triangle, not just a right triangle. If you've got the Law of Sines and the Law of Cosines under your belt, .... I've written a TI-83/84 program to solve all types of triangles
The Law of Sines
We use the Law of Sines and the Law of Cosines to solve triangles that are not right-angled. Such triangles are called oblique or scalene triangles.
The Law of Cosines
We use the Law of Cosines to solve triangles that are not right-angled. In particular, when we know two sides of a triangle and their included angle, then the Law of Cosines enables us to find the third side.
math programs, and finance tutorials for the TI-83, and TI-84 calculators.
Find Triangle Sides and Angles (using Law of Cosines and Law of Sines)
 

Trigonometric Identities

List of trigonometric identities
In mathematics, trigonometric identities are equalities that involve trigonometric functions that are true for every single value of the occurring variables.
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. These identities mostly refer to one angle denoted t, but there are a few of them involving two angles, and for those, the other angle is denoted s..
Trig Identities
Identities involving trig functions are listed below.
Table of Trigonometric Identities
Reciprocal identities, Pythagorean Identities, Quotient Identities, Co-Function Identities, Even-Odd Identities, Sum-Difference Formulas, Double Angle Formulas, Power-Reducing/Half Angle Formulas, Sum-to-Product Formulas, Product-to-Sum Formulas
Trigonometric Identities
Free math lessons and math homework help from basic math to algebra, geometry and beyond.
Trigonometric Identities
An Idenity is an Equality that is true for any value of the variable.
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Clep Study Guides

College Algebra
Free University Project - The CLEP Exam in Algebra is similar to a one semester course taught at many colleges.
Mathematics
Free University Project -The College Mathematics CLEP is very broad in scope. It is similar to a one year survey course taught at many colleges.
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Trigonometry
Wikibooks has a book on Trigonometry
Trigonometric function
Wikibooks has a book on Trigonometric function
Trigonometric identity
Wikibooks has a book on Trigonometric identity
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