I. Introduction
Trigonometry is the math of angles and periodic behavior. It connects triangles and circles to define the trigonometric functions, and it’s the foundation for modeling waves, rotations, oscillations, and many real-world measurements.
II. Outline
- I - Right Triangle Basics
- Angles, degrees vs radians
- Similar triangles & trigonometric ratios (sin, cos, tan)
- Solving right triangles (unknown sides/angles)
- Applications (height/distance, navigation, inclines)
- II - The Unit Circle & Graphs
- Unit circle definitions of trig functions
- Reference angles and quadrants (signs of trig values)
- Exact values at special angles
- Graphs of sin/cos/tan (amplitude, period, phase shift, vertical shift)
- Inverse trig functions and their domains/ranges
- III - Identities & Algebra with Trig
- Reciprocal, quotient, and Pythagorean identities
- Even/odd and periodic properties
- Sum/difference formulas
- Double-angle and half-angle formulas
- Proving identities (strategy)
- IV - Equations, Triangles, and Modeling
- Solving trig equations
- Law of Sines and Law of Cosines
- Area formulas
- Sinusoidal modeling (waves, sound, AC circuits, seasons)
- Polar coordinates & basic complex-number connection
III. Free Books
- College Trigonometry pdf
- Utah Universities’ Trigonometry pdf
- Algebra and Trigonometry 2e
- Chapter 7-10
- Paul’s Online Math Notes — Algebra/Trig Review
