32 free lessons · A guided path
Trigonometry
Find the rhythm in the world.
Connect angles and triangles to circles, motion, waves, and the building blocks of signals.
Explore the path ↓Find a comfortable starting point
One subject. Many levels of understanding.
Start with a familiar idea and move forward when the reasoning feels clear. Each lesson states its prerequisites. Grade is your first guide; the stages below describe the challenge within this subject, rather than a single school year. Extension lessons introduce selected advanced topics.
Foundations
Build intuition, name the quantities, and explain the basic idea.
2 lessons
Developing
Connect familiar ideas and choose a useful representation for a problem.
2 lessons
Intermediate
Combine methods, compare approaches, and justify the steps you take.
17 lessons
Advanced
Use deeper tools and check the assumptions behind a model or argument.
9 lessons
Extension
Meet selected university and research ideas after reviewing their prerequisites.
2 lessons
Your trigonometry lesson library
Choose the idea you want to explore.
Filter by grade or topic difficulty, or search for a particular skill. The collection includes every trigonometry lesson, with 12 shown at a time so you can browse at your own pace.
Showing 12 of 32 matching lessons · All free
TrigonometryGrade 10 · Intermediate 12 min
See why side-side-angle can give two triangles
Use sine symmetry to identify two valid triangle configurations.
Read, practice, and reflectTrigonometryGrade 10 · Intermediate 12 min
Choose sine, cosine, or tangent from the known sides
Match a right-triangle ratio to a chosen reference angle.
Read, practice, and reflectTrigonometryGrade 10 · Intermediate 12 min
Recover an angle from a measured ratio
Use an inverse trigonometric function with consistent angle units.
Read, practice, and reflectTrigonometryGrade 10 · Intermediate 12 min
Extend Pythagoras to a nonright triangle
Use the cosine rule with an included angle.
Read, practice, and reflectTrigonometryGrade 10 · Intermediate 12 min
Use a known opposite side-angle pair
Match corresponding sides and opposite angles in the sine rule.
Read, practice, and reflectTrigonometryGrade 10 · Intermediate 12 min
Find area without a stated altitude
Express a triangle's height using sine of the included angle.
Read, practice, and reflectTrigonometryGrade 11 · Intermediate 13 min
Find an exact trigonometric value from familiar angles
Apply an angle-addition identity instead of rounding early.
Read, practice, and reflectTrigonometryGrade 11 · Intermediate 13 min
Keep quadrant information in a double-angle calculation
Find a doubled angle's sine and cosine without guessing its quadrant.
Read, practice, and reflectTrigonometryGrade 11 · Intermediate 13 min
State where a simplified identity is actually defined
Preserve domain restrictions while simplifying a trigonometric quotient.
Read, practice, and reflectTrigonometryGrade 11 · Intermediate 13 min
List every solution of a periodic equation
Combine reference-angle solutions with full-period shifts.
Read, practice, and reflectTrigonometryGrade 11 · Intermediate 13 min
Recognize an inverse trigonometric function's chosen output range
Reduce a composition to its principal angle rather than cancelling blindly.
Read, practice, and reflectTrigonometryGrade 11 · Intermediate 13 min
Separate horizontal shift from angular frequency
Read a factored sinusoidal model's amplitude, period, and phase shift.
Read, practice, and reflectGive the idea a shape.
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