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The six trigonometric functions from the right triangle to the unit circle, their graphs, identities and equations, then the laws of sines and cosines, vectors, polar coordinates and complex numbers.
Before this: Algebra 2 What you'll be able to do
Evaluate trig functions exactly at special angles Graph sinusoids and their transformations Verify identities and solve trig equations Solve any triangle Start the course
Go through each topic step by step — prose, worked examples, quick checks, and a timed practice round after every section.
Every test ends with a score by topic and a list of what to revisit. Test out of a topic with 80% or better to mark it mastered.
Topics 1. Core Ideas in Plain Terms
5 lessons The big trig ideas, in everyday language
2. Law of Sines and Law of Cosines
7 lessons Solving oblique triangles: AAS, ASA, SSA, SAS, SSS, area, and applications
3. Vectors and the Dot Product
8 lessons Components, magnitude & direction, the dot product, projection, and applications
4. Polar Coordinates and Complex Numbers
8 lessons Plotting, conversions, polar graphs, trig form, products, and DeMoivre's Theorem
5. Angles and Their Measure
9 lessons Standard position, radians, arc length, sector area, and speed
6. Right Triangle Trigonometry
7 lessons The six ratios, special angles, solving triangles, cofunctions, and applications
7. The Unit Circle and Circular Functions
8 lessons Special angles, reference angles, signs, periodicity, even/odd, and terminal points
8. Graphs of Sine and Cosine
8 lessons Amplitude, period, phase shift, vertical shift, and modeling
9. Graphs of the Other Trigonometric Functions
6 lessons Tangent, cotangent, secant, and cosecant: periods, asymptotes, and transformations
10. Inverse Trigonometric Functions
8 lessons Definitions, exact values, compositions, graphs & equations
11. Trigonometric Identities
7 lessons Fundamental identities, simplifying, and verifying
12. Sum, Difference, and Multiple-Angle Formulas
9 lessons Exact values, double & half-angles, power-reducing, product-to-sum
13. Trigonometric Equations
8 lessons Basic equations, factoring, quadratic form, identities, multiple angles, and inverses
14. Course Review
12 lessons Every definition, rule, and formula from all twelve topics in one place