Precalculus Trigonometry
Bridge the gap between triangle geometry and continuous waves. Learn how sine, cosine, and tangent power circular motion, periodic graphing, and algebraic identities for advanced math.
Like Duolingo, but for Precalculus Trigonometry. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
27 levels across 3 sections, about 54 minutes end to end, roughly 11 days at five minutes a day. It moves through Unlocking the Unit Circle, Graphing and Shaping Periodic Waves, and Solving Equations and Transforming Expressions. It assumes you already know the basics.
Free forever · No credit card · iPhone & Android
Key ideas in Precalculus Trigonometry
- A unit circle has a radius of exactly one unit by definition
- Radian value equals the subtended arc length along a unit circle
- Radian measure eliminates arbitrary degree scaling factors
- Arc length equals the circle radius multiplied by angle in radians
- The formula s = r * theta requires angle measurement strictly in radians
- Multiplying radius by radian angle bypasses 360-degree fractions
- Pi radians represents a half-turn or a straight line across the circle
- Fractions between 1/2 and 1 of pi naturally sit in Quadrant II
- Fractions between 1 and 3/2 of pi naturally sit in Quadrant III
- Fractions between 3/2 and 2 of pi naturally sit in Quadrant IV
- Pi over 6 represents one-twelfth of a circle or one-third of a quadrant
- Adding or subtracting full rotations of 2pi yields coterminal angles
- Negative signs indicate clockwise rotation from the standard initial axis
- Angles beyond 2pi wrap repeatedly around the circular coordinate plane
- A hypotenuse of one eliminates division when computing adjacent and opposite sides
- The horizontal displacement x corresponds directly to cosine on a unit circle
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives Precalculus Trigonometry the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
You walk along the rim of a unit circle through a central angle of 2.5 radians. How far have you walked?
Get it right to open this lesson and 26 more in the app.
How to learn Precalculus Trigonometry, step by step
Go in order. 27 short levels across 3 sections, about 54 minutes in all, five minutes a day.
- 1
Unlocking the Unit Circle
- Radians and Circular Angle Measurement
- The Unit Circle as a Coordinate Engine
- 2
Graphing and Shaping Periodic Waves
- Graphing Sine and Cosine as Oscillations
- Phase Shifts and Tangent Discontinuities
- Modeling Periodic Systems
- 3
Solving Equations and Transforming Expressions
- Inverse Functions and Multi-Valued Solutions
- Algebraic Manipulation with Fundamental Identities
- Angle Sum and Double-Angle Mechanics
3 sections · 8 units · 27 levels. Built to play, not to enroll.
Questions about Precalculus Trigonometry
How do I learn Precalculus Trigonometry?
Go in order: start with Unlocking the Unit Circle, then Graphing and Shaping Periodic Waves, then Solving Equations and Transforming Expressions. On Tomo that's 27 short levels, about 54 minutes in all, played five minutes a day. Start free and play the first level in under a minute.
Is there a Duolingo-style app for Precalculus Trigonometry?
Yes. Tomo works like Duolingo: short daily lessons, streaks and quick quizzes. Precalculus Trigonometry is one of its free courses, and you can type any other topic to get a course of your own.
Is the Precalculus Trigonometry course free?
Yes. Precalculus Trigonometry is playable on Tomo's free plan, which doesn't expire. No credit card, no waitlist. Download the app and start your first lesson.
How long does it take to learn Precalculus Trigonometry?
27 levels across 3 sections, about 54 minutes of play in total. It's built for five minutes a day, so you finish it a little at a time instead of all at once.
Do I need any background to start Precalculus Trigonometry?
No. It's pitched at an intermediate level, so it starts where you are and builds up. If you can tap a phone, you can start.
Tomo is in ChatGPT
Tomo is also a ChatGPT plugin: the same playable courses, built and played inside your chat.
Add Tomo to ChatGPT- What to ask
- “Make me a Tomo course on black holes.” “Turn this chat into a Tomo course.”
- What you get
- Quick questions with instant feedback, hearts and stars, ready to play in about a minute.
- Where it goes
- No sign-up to start. Connect your Tomo account and your streak carries on in the app.
You pick the voice
Precalculus Trigonometry is taught in the Professor style: clear, structured, thorough. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
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Start Precalculus Trigonometry today.
Download Tomo, search Precalculus Trigonometry, and play your first lesson in under a minute.