Trigonometry
Trigonometry is the math of angles and triangles — specifically, the relationships between angles and side lengths. It extends what you learned in geometry into a powerful toolkit used in construction, engineering, navigation, physics, and dozens of other fields.
Why Trigonometry Matters
Trig is everywhere in technical work:
- Carpenters use trig to calculate roof pitch, rafter lengths, and stair angles
- Electricians use trig for conduit bending angles and AC circuit analysis
- Surveyors use trig to measure distances and heights indirectly
- HVAC technicians use trig for ductwork angles and airflow calculations
- Machinists use trig for precision angle cuts and gear calculations
It’s also one of the most-tested subjects on the SAT, ACT, and GED math sections.
Where to Start
Start with SOH CAH TOA — the three basic trig ratios are the foundation everything else builds on. Then move to finding missing sides and angles, which is where trig becomes immediately practical. If you’re preparing for the SAT/ACT, prioritize SOH CAH TOA, special angles, and the unit circle.
Topics in this section
Foundations
Introduction to Trigonometry · SOH CAH TOA · Finding Missing Sides with Trigonometry · Finding Missing Angles · When to Use Sine, Cosine, or Tangent · Angles of Elevation and Depression · Trig Values of Special Angles
7 topicsUnit Circle
The Unit Circle · Radians and Degrees · How to Memorize the Unit Circle
3 topicsGraphing
Graphs of Sine and Cosine · Graphs of Tangent, Cotangent, Secant, and Cosecant · Sinusoidal Modeling
3 topicsIdentities
Trigonometric Identities · Sum, Difference, and Double-Angle Formulas · Half-Angle and Power-Reducing Formulas · How to Prove Trig Identities: A Strategy Guide
4 topicsSolving Triangles
Law of Sines · Law of Cosines · Triangle Area Formulas: ½ab sin C and Heron's Formula
3 topicsMistakes And Practice
Common Trigonometry Mistakes and How to Avoid Them
1 topicInverse Functions
Inverse Trigonometric Functions
1 topicEquations
Solving Trigonometric Equations · Advanced Trigonometric Equations
2 topicsLast updated: March 28, 2026