Intro to Trigonometry
About this free Intro to Trigonometry course
Intro to Trigonometry is a free online trigonometry course that uncovers the hidden math behind angles, triangles, and waves. It guides you from right triangle ratios to the unit circle, graphs of sine and cosine, trigonometric equations, and identities.
Along the way, you'll see how trig connects to real-world phenomena, from engineering and architecture to music and how GPS pinpoints your location. Interactive slide lessons include worked examples and practice problems, and short companion videos on the STEM for Others YouTube channel give memorable walkthroughs of ideas like radians and the Pythagorean identity.
Who this course is for
The course is for high school students in grades 10 through 12 who have completed Geometry and are taking or have finished Algebra 2. It's also a solid review before precalculus or Intro to Calculus.
Course outline
- Unit 1: Right triangle trigonometry. Sine, cosine, and tangent ratios, special right triangles, and solving right triangles.
- Unit 2: Trigonometric functions of any angle. Radians, reference angles, and the unit circle.
- Unit 3: Trigonometry in any triangle. The Law of Sines, the Law of Cosines, and finding the area of a triangle.
- Unit 4: Graphs of trigonometric functions. Amplitude, period, phase shift, and graphing sine, cosine, and tangent.
- Unit 5: Trigonometric equations. Solving trig equations and finding all solutions in an interval.
- Unit 6: Trigonometric identities. Pythagorean, sum and difference, and double-angle identities, and verifying identities.
What you'll learn
- Solve right and oblique triangles using trig ratios and the Laws of Sines and Cosines
- Convert between degrees and radians and use the unit circle fluently
- Graph and transform sine, cosine, and tangent functions
- Solve trigonometric equations
- Prove and apply fundamental trigonometric identities
How long it takes
Expect about 20 hours: roughly three hours per unit, including practice. The video lessons add about 30 minutes and are a great way to review before a test.
Frequently asked questions about Intro to Trigonometry
Is Intro to Trigonometry really free?
Yes. Intro to Trigonometry is completely free, with no fees, subscriptions, or account required. STEM for Others is a 501(c)(3) nonprofit, and every course in our curriculum library is free for students, families, and teachers.
Where is trigonometry used in real life?
Trigonometry is behind GPS, architecture and surveying, sound and music, computer graphics, and engineering. Any time something repeats in cycles, like waves, rotations, or seasons, trig functions describe it.
How do I start the course?
Click Begin Course at the top of this page to open the full slide deck, and use the companion video lessons on the STEM for Others YouTube channel when you want a walkthrough. Work through one unit at a time and try the practice questions before moving on.
Do I get a certificate?
The self-paced Intro to Trigonometry materials don't include an official certificate. If you're taking the course through a STEM for Others chapter program, ask your chapter leader about recognizing your completion.
Can teachers and clubs use this curriculum?
Yes. Teachers, homeschool families, libraries, and after-school clubs are welcome to use the Intro to Trigonometry materials with their students at no cost. STEM for Others volunteers also teach our curriculum in partner schools and libraries. You can find a chapter near you or start one at your school.
