bythreedu · Math Tracks · Curriculum v1.0 · 2026

Angles, circles,
and the mathematics
of periodic phenomena.

A complete Trigonometry course from radian measure and the unit circle through inverse functions and real-world applications. Built for students heading into precalculus or calculus who need trig to feel like a tool, not a memorization exercise.

Total Lessons18at your pace
Units6progressive phases
Assignments6+problem sets
DestinationPrecalculus
Ready
00Approach
Course Philosophy

Derive, Don't Memorize

The trig identities in this course are derived, not listed. The unit circle is built from scratch in the first unit, not copied from a reference sheet. Students who understand where the formulas come from can reconstruct any identity they forget — and forget far fewer of them.

The Unit Circle Is the Foundation

Every trig concept in this course — functions, graphs, identities, equations, inverses — connects back to the unit circle. Students who truly own the unit circle do not need to memorize the individual values; they reconstruct them. This course makes that happen.

01Curriculum
Learning Path
01
Unit 1 · Weeks 1–3
Angles, Radians, and the Unit Circle
3 lessons · Angle measure · Unit circle · Trig functions defined
radian measureunit circlesix trig functions
+
02
Unit 2 · Weeks 4–6
Trig Graphs
3 lessons · Sin and cos graphs · Other trig graphs · Transformations
amplitudeperiodphase shift
+
03
Unit 3 · Weeks 7–9
Trig Identities
3 lessons · Fundamental identities · Sum and difference · Double and half angle
Pythagorean identitiessum formulasdouble angle
+
04
Unit 4 · Weeks 10–12
Solving Trig Equations
3 lessons · Basic trig equations · Equations requiring identities · General solutions
general solutionprincipal valueidentity substitution
+
05
Unit 5 · Weeks 13–15
Triangle Trigonometry
3 lessons · Right triangles · Law of Sines · Law of Cosines
SOH-CAH-TOAambiguous caselaw selection
+
06
Unit 6 · Weeks 16–18
Inverse Trig Functions and Capstone
2 lessons + capstone · Inverse functions · Applications · Final review
restricted domaininverse compositionreal-world modeling
+
02Capstone
Final Exam Simulation

The capstone is a timed 75-minute problem set across all 6 units. Every missed problem gets a written correction with the reasoning that should have driven each step. The goal is to walk into precalculus with trig feeling like a tool.

○
Gap Review
Two weakest units revisited before the exam simulation.
○
Timed Final Exam
Full-length, independent, same conditions as a real exam.
○
Written Corrections
Every missed problem corrected with reasoning — not just the right answer.
○
Precalculus Readiness Review
A final session on what Precalculus will demand from day one.
03Investment
Pricing Options
Location
per Session
$125
1.5 hrs · online only
Session length
  • —Flexible scheduling
  • —1-on-1 focused attention
  • —No long-term commitment

Best for trying the curriculum before committing to a plan.

Popular
per Month
$500
4 sessions · 1.5 hrs/session
Frequency
Session length
  • —Session notes after every lesson
  • —Async DM support between sessions
  • —Priority scheduling

Adjust frequency and session length above — price updates automatically.

Per Semester
$2,000
16 sessions · 1.5 hrs/session
Term length
Frequency
Session length
  • —All 6 units — full course arc
  • —Session notes after every lesson
  • —Capstone exam simulation + written corrections
  • —Precalculus readiness review at completion

The full Trigonometry arc in one commitment.

📍
In-person available · NYC onlyMonthly and semester plans can be done in-person. Select “In-person · NYC” above to see adjusted pricing.
04Contact
Let's Talk

Heading into precalculus or struggling with trig? One session shows exactly where the gaps are.

What do I need to know coming in?+
Are lessons online or in-person?+
Can I switch plans later?+
What if I need to reschedule?+