Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Trigonometry
Topic: The Six Trigonometric Functions
Subtopic: Triangles

Overview

As you may suspect "trigonometry" is strongly tied to the study of "triangles", their measurement, and their relationships. In this section we develop the main theorems regarding triangles. Watch which involve right triangles only and which are more general.

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 1.2.1 Solve problems using the "180° in a triangle" theorem
• 1.2.2 Solve problems using the Pythagorean theorem
• 1.2.3 Recognize and use the two "special" triangles (45°-45°-90° and 30°-60°-90°)
• 1.2.4 Recognize and use Pythagorean triples

Terminology

Terms you should be able to define: right triangle, hypotenuse, (triangle's) leg, acute triangle, obtuse triangle, equilateral triangle, equiangular triangle, isosceles triangle, theorem

Memorize the Pythagorean Theorem and know that while "a" and "b" are interchangable, "c" always represents the hypotenuse: a^2+b^2=c^2

Memorize the relationship of the sides on the two "special" triangles: Text Notes

The e-textbook may cover several definitions and theorems from geometry (eg, the alternate interior angle theorem). These should be review from a high school geometry course. Skim as needed.

Mini-Lectures and Examples

Supplementary Resources (recommended)

The following links are for exploration. No need to explore them all, but pick at least two that interest you. Information on Pythagoras, the Pythagorean Theorem, and Pythagorean Triples:

 The Pythagorean theorem can be seen in terms of areas. In reference to the image at the right, the area of the yellow square (at the bottom) is a^2, the area of the blue square (at the right) is b^2, and these two areas together equal the area of the green square (tilted on the left top), c^2, thus a^2+b^2=c^2. This holds no matter how big the original red triangle (in the middle) is as long as it is a right triangle. Neat, aye? This little video shows this area relationship using water. I want one of these! www.youtube.com/watch?v=CAkMUdeB06o

Supplemental Resources (optional)

Videos from James Sousa's MathIsPower4U:

Animation: The Sum of the Interior Angles of a Triangle
Mini-lesson: Angle Relationships and Types of Triangles

rev. 2020-09-12