School Launch

Scope and sequence · Math

Trigonometry

The measure of triangles and circles, from Euclid to the unit circle, for surveying, building, navigation and science

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What to cover

40 of 48 lessons are MUST COVER. They are tested on the unit tests and exams, or are skills the SAT/ACT relies on. OPTIONAL lessons are enrichment. Do them if time allows. The course is complete when the MUST COVER lessons are done.

Unit 1: Right-Triangle Trigonometry

  • MUST COVER 1.1 Similar Right Triangles and the Idea of a Ratio · SAT/ACT
  • MUST COVER 1.2 Sine, Cosine and Tangent · exam, SAT/ACT
  • MUST COVER 1.3 Finding Unknown Sides · exam
  • MUST COVER 1.4 Finding Unknown Angles · exam
  • MUST COVER 1.5 The Reciprocal Ratios · exam, SAT/ACT

Unit 2: Special Right Triangles and Exact Values

  • MUST COVER 2.1 The 45-45-90 Triangle · exam, SAT/ACT
  • MUST COVER 2.2 The 30-60-90 Triangle · exam, SAT/ACT
  • MUST COVER 2.3 Complementary Angles and Cofunctions · exam, SAT/ACT

Unit 3: Angles, Radians and the Unit Circle

  • MUST COVER 3.1 Angles in Standard Position · exam
  • OPTIONAL 3.2 Radian Measure
  • MUST COVER 3.3 Converting Degrees and Radians · exam
  • MUST COVER 3.4 Arc Length and Sector Area · exam, SAT/ACT
  • MUST COVER 3.5 Linear and Angular Speed · exam, SAT/ACT
  • MUST COVER 3.6 The Unit Circle · exam, SAT/ACT
  • MUST COVER 3.7 Reference Angles and Signs by Quadrant · exam
  • MUST COVER 3.8 Exact Values Around the Unit Circle · exam, SAT/ACT

Unit 4: Graphs of the Trigonometric Functions

  • MUST COVER 4.1 The Graph of Sine · SAT/ACT
  • MUST COVER 4.2 The Graph of Cosine · SAT/ACT
  • MUST COVER 4.3 Amplitude and Period · exam
  • MUST COVER 4.4 Phase Shift and Vertical Shift · exam
  • MUST COVER 4.5 Writing Sinusoidal Equations · exam, SAT/ACT
  • MUST COVER 4.6 The Graph of Tangent · exam
  • MUST COVER 4.7 Graphs of Cosecant, Secant and Cotangent · exam

Unit 5: Trigonometric Identities

  • OPTIONAL 5.1 Fundamental Identities
  • MUST COVER 5.2 The Pythagorean Identities · exam, SAT/ACT
  • MUST COVER 5.3 Simplifying and Proving Identities · exam
  • MUST COVER 5.4 Sum and Difference Formulas · exam
  • MUST COVER 5.5 Double-Angle and Half-Angle Formulas · exam

Unit 6: Inverse Functions and Trigonometric Equations

  • MUST COVER 6.1 Inverse Sine and Restricted Domains · SAT/ACT
  • MUST COVER 6.2 Inverse Cosine and Inverse Tangent · exam, SAT/ACT
  • MUST COVER 6.3 Compositions with Inverse Functions · exam, SAT/ACT
  • MUST COVER 6.4 Solving Basic Trigonometric Equations · exam, SAT/ACT
  • MUST COVER 6.5 Equations Using Factoring, Identities and Multiple Angles · exam, SAT/ACT

Unit 7: Oblique Triangles: The Laws of Sines and Cosines

  • MUST COVER 7.1 The Area of a Triangle · exam, SAT/ACT
  • MUST COVER 7.2 The Law of Sines · exam, SAT/ACT
  • MUST COVER 7.3 The Ambiguous Case (SSA) · exam
  • MUST COVER 7.4 The Law of Cosines · exam, SAT/ACT
  • MUST COVER 7.5 Solving Any Triangle · SAT/ACT

Unit 8: Applications

  • MUST COVER 8.1 Angles of Elevation and Depression · exam
  • MUST COVER 8.2 Bearings and Navigation · exam
  • MUST COVER 8.3 Surveying and Triangulation · exam
  • OPTIONAL 8.4 Problems in Three Dimensions
  • MUST COVER 8.5 Modeling Periodic Motion · exam

Unit 9: Polar Coordinates and Vectors OPTIONAL unit

  • OPTIONAL 9.1 Polar Coordinates
  • OPTIONAL 9.2 Converting Between Polar and Rectangular Form
  • OPTIONAL 9.3 Graphing Polar Equations
  • OPTIONAL 9.4 Vectors: Magnitude, Direction and Components
  • OPTIONAL 9.5 Vector Applications

36-week pacing calendar

This is a 18-week course. Pair it with another course in the same subject, or spread it over the year at a lighter pace.

WeekPlanDoneNotes
Wk 1Day 1: Lesson 1.1 Similar Right Triangles and the Idea of a Ratio
Day 2: Lesson 1.2 Sine, Cosine and Tangent
Day 3: Lesson 1.3 Finding Unknown Sides (day 1 of 2)
Day 4: Lesson 1.3 Finding Unknown Sides (day 2 of 2)
Day 5: Lesson 1.4 Finding Unknown Angles (day 1 of 2)
Wk 2Day 6: Lesson 1.4 Finding Unknown Angles (day 2 of 2)
Day 7: Lesson 1.5 The Reciprocal Ratios
Day 8: Unit 1 review
Day 9: Unit 1 test
Day 10: Lesson 2.1 The 45-45-90 Triangle
Wk 3Day 11: Lesson 2.2 The 30-60-90 Triangle
Day 12: Lesson 2.3 Complementary Angles and Cofunctions (day 1 of 2)
Day 13: Lesson 2.3 Complementary Angles and Cofunctions (day 2 of 2)
Day 14: Unit 2 review
Day 15: Unit 2 test
Wk 4Day 16: Lesson 3.1 Angles in Standard Position
Day 17: Lesson 3.2 Radian Measure
Day 18: Lesson 3.3 Converting Degrees and Radians
Day 19: Lesson 3.4 Arc Length and Sector Area (day 1 of 2)
Day 20: Lesson 3.4 Arc Length and Sector Area (day 2 of 2)
Wk 5Day 21: Lesson 3.5 Linear and Angular Speed (day 1 of 2)
Day 22: Lesson 3.5 Linear and Angular Speed (day 2 of 2)
Day 23: Lesson 3.6 The Unit Circle (day 1 of 2)
Day 24: Lesson 3.6 The Unit Circle (day 2 of 2)
Day 25: Lesson 3.7 Reference Angles and Signs by Quadrant
Wk 6Day 26: Lesson 3.8 Exact Values Around the Unit Circle (day 1 of 2)
Day 27: Lesson 3.8 Exact Values Around the Unit Circle (day 2 of 2)
Day 28: Unit 3 review
Day 29: Unit 3 test
Day 30: Lesson 4.1 The Graph of Sine
Wk 7Day 31: Lesson 4.2 The Graph of Cosine
Day 32: Lesson 4.3 Amplitude and Period (day 1 of 2)
Day 33: Lesson 4.3 Amplitude and Period (day 2 of 2)
Day 34: Lesson 4.4 Phase Shift and Vertical Shift (day 1 of 2)
Day 35: Lesson 4.4 Phase Shift and Vertical Shift (day 2 of 2)
Wk 8Day 36: Lesson 4.5 Writing Sinusoidal Equations (day 1 of 2)
Day 37: Lesson 4.5 Writing Sinusoidal Equations (day 2 of 2)
Day 38: Lesson 4.6 The Graph of Tangent
Day 39: Lesson 4.7 Graphs of Cosecant, Secant and Cotangent
Day 40: Unit 4 review
Wk 9Day 41: Unit 4 test
Day 42: Midterm review (Units 1–4)
Day 43: Midterm exam (Units 1–4)
Day 44: Lesson 5.1 Fundamental Identities
Day 45: Lesson 5.2 The Pythagorean Identities
Wk 10Day 46: Lesson 5.3 Simplifying and Proving Identities (day 1 of 2)
Day 47: Lesson 5.3 Simplifying and Proving Identities (day 2 of 2)
Day 48: Lesson 5.4 Sum and Difference Formulas (day 1 of 2)
Day 49: Lesson 5.4 Sum and Difference Formulas (day 2 of 2)
Day 50: Lesson 5.5 Double-Angle and Half-Angle Formulas (day 1 of 2)
Wk 11Day 51: Lesson 5.5 Double-Angle and Half-Angle Formulas (day 2 of 2)
Day 52: Unit 5 review
Day 53: Unit 5 test
Day 54: Lesson 6.1 Inverse Sine and Restricted Domains
Day 55: Lesson 6.2 Inverse Cosine and Inverse Tangent
Wk 12Day 56: Lesson 6.3 Compositions with Inverse Functions
Day 57: Lesson 6.4 Solving Basic Trigonometric Equations (day 1 of 2)
Day 58: Lesson 6.4 Solving Basic Trigonometric Equations (day 2 of 2)
Day 59: Lesson 6.5 Equations Using Factoring, Identities and Multiple Angles (day 1 of 2)
Day 60: Lesson 6.5 Equations Using Factoring, Identities and Multiple Angles (day 2 of 2)
Wk 13Day 61: Unit 6 review
Day 62: Unit 6 test
Day 63: Lesson 7.1 The Area of a Triangle
Day 64: Lesson 7.2 The Law of Sines
Day 65: Lesson 7.3 The Ambiguous Case (SSA) (day 1 of 2)
Wk 14Day 66: Lesson 7.3 The Ambiguous Case (SSA) (day 2 of 2)
Day 67: Lesson 7.4 The Law of Cosines (day 1 of 2)
Day 68: Lesson 7.4 The Law of Cosines (day 2 of 2)
Day 69: Lesson 7.5 Solving Any Triangle
Day 70: Unit 7 review
Wk 15Day 71: Unit 7 test
Day 72: Lesson 8.1 Angles of Elevation and Depression
Day 73: Lesson 8.2 Bearings and Navigation (day 1 of 2)
Day 74: Lesson 8.2 Bearings and Navigation (day 2 of 2)
Day 75: Lesson 8.3 Surveying and Triangulation (day 1 of 2)
Wk 16Day 76: Lesson 8.3 Surveying and Triangulation (day 2 of 2)
Day 77: Lesson 8.4 Problems in Three Dimensions
Day 78: Lesson 8.5 Modeling Periodic Motion
Day 79: Unit 8 review
Day 80: Unit 8 test
Wk 17Day 81: Lesson 9.1 Polar Coordinates (optional Unit 9; families who skip it review Units 1–2 today)
Day 82: Lesson 9.2 Converting Between Polar and Rectangular Form (optional Unit 9; families who skip it review Unit 3 today)
Day 83: Lesson 9.3 Graphing Polar Equations (optional Unit 9; families who skip it review Unit 4 today)
Day 84: Lesson 9.4 Vectors: Magnitude, Direction and Components (optional Unit 9; families who skip it review Units 5–6 today)
Day 85: Lesson 9.5 Vector Applications (optional Unit 9; families who skip it review Units 7–8 today)
Wk 18Day 86: Unit 9 review (optional; families who skip Unit 9 do a cumulative review of Units 1–8)
Day 87: Unit 9 test (optional; families who skip Unit 9 rework missed unit-test problems)
Day 88: Final exam review, Units 1–4
Day 89: Final exam review, Units 5–8
Day 90: Final exam (Units 1–8)
Wk 19Open week: second course, project or review
Wk 20Open week: second course, project or review
Wk 21Open week: second course, project or review
Wk 22Open week: second course, project or review
Wk 23Open week: second course, project or review
Wk 24Open week: second course, project or review
Wk 25Open week: second course, project or review
Wk 26Open week: second course, project or review
Wk 27Open week: second course, project or review
Wk 28Open week: second course, project or review
Wk 29Open week: second course, project or review
Wk 30Open week: second course, project or review
Wk 31Open week: second course, project or review
Wk 32Open week: second course, project or review
Wk 33Open week: second course, project or review
Wk 34Open week: second course, project or review
Wk 35Open week: second course, project or review
Wk 36Open week: second course, project or review

Grading: Practice sets 20%, Unit tests 40%, Midterm exam 15%, Final exam 20%, Notebook and corrections 5%. Scale: A 90–100, B 80–89, C 70–79, D 60–69, below 60 redo