Unit 10 · 4 Weeks · 10 Lessons
Trigonometric Functions & Periodic Models
How do angle measure, the unit circle, graphs, and periodic functions model rotation, waves, cycles, and repeated behavior?
Complete instructional sequence
Detailed Lessons
Lessons include objectives, formulas, concept development, worked examples, guided and independent practice, differentiated pathways, application, misconception analysis, mastery evidence, reflection, and local completion.
Angle Measure, Radians & Coterminal Angles
Radians measure angle by arc length relative to radius. Coterminal angles differ by full rotations, and reference angles connect positions to exact values.
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Lesson 02The Unit Circle & Coordinate Definitions
The unit circle defines sine and cosine as coordinates and all other trigonometric functions as ratios. Symmetry and reference angles reduce memorization.
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Lesson 03Exact Trigonometric Values & Reference Angles
Exact trigonometric values come from special triangles and unit-circle symmetry. Keep radicals exact unless approximation is requested.
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Lesson 04Six Trigonometric Functions & Reciprocal Relationships
The six trigonometric functions are connected by quotient and reciprocal relationships. Undefined values occur when denominators are zero.
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Lesson 05Graphs of Sine and Cosine
Sine and cosine graphs encode periodic change. Key points at quarter-period intervals support accurate sketches and interpretation.
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Lesson 06Amplitude, Period, Phase & Vertical Shifts
A controls vertical scale, B controls period, C phase shift, and D midline. Context determines which features have physical meaning.
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Lesson 07Graphs of Tangent, Cotangent, Secant & Cosecant
Tangent and cotangent have vertical asymptotes and no amplitude. Secant and cosecant are reciprocal graphs with branches outside |y|≥1.
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Lesson 08Inverse Trigonometric Functions & Restricted Domains
arcsin, arccos, and arctan return principal angles. They reverse trig functions only within specified ranges.
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Lesson 09Sinusoidal Regression & Periodic Data
Periodic regression estimates amplitude, cycle length, phase, and midline. Data span should cover enough cycles to support the model.
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Lesson 10Vectors, Bearings & Component Models
Vectors represent magnitude and direction. Components add, scalar multiplication changes magnitude and possibly direction, and bearings require careful angle conventions.
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Practice and evidence
Unit Resources
Foundation Practice
Prerequisite support, smaller steps, representation aids, and correction prompts.
Core Practice
Complete standards-level definitive-answer practice and explanation.
Extended Practice
Generalization, proof, parameter analysis, technology, and deeper modelling.
Unit Mastery Check
Fresh randomized questions with scoring and explanations.
Periodic Phenomenon Modelling Studio
Applied investigation with evidence, validation, limitations, and defense.
Family Guide
Plain-language overview, support questions, and evidence expectations.
Teacher Guide
Pacing, differentiation, assessment, misconceptions, and records.
Vocabulary Data
Core English terms with Spanish, French, Arabic, and Portuguese support.
Standards Map
Unit concepts and broad national/international alignment categories.