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trigonometry academic library 

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​Trigonometry is a six-unit elective honors course for high school students who have successfully completed Algebra I, Geometry, and Algebra II. The materials cover a development of trigonometry from right triangle trigonometry to oblique triangles and the polar plane.

​Throughout the course, students will develop trigonometric formulas and use them in real-world applications, evaluate trigonometric proofs using complex trigonometric identities and solving trigonometric equations with regard to the unit circle.

trigonometry online

UNIT 1 - RIGHT TRIANGLE TRIGONOMETRY
UNIT 2 - GRAPHING AND INVERSE FUNCTIONS
  1. Course Overview
  2. Lengths of Sides
    • Basic Trigonometry      
    • Introduction to Trigonometric Functions Using Triangles   
  3. Angle Measures
    • Introduction to Inverse Trigonometric Functions  
    • Introduction to Inverse Sine, Inverse Cosine, Inverse Tangent  
  4. Indirect Measure
    • Angle of Elevation and Depression  
    • Indirect Measurement Using Similar Triangles    
  5. Quiz 1: Solving a Right Triangle
  6. Angles in the Coordinate Plane
    • Coterminal Angles - Example 1  
  7. The Unit Circle
    • Introduction to the unit circle  
  8. Trigonometric Values of Special Angles
    • Evaluating Sine, Cosine and Tangent at 30, 45, and 60 Degrees (mini lesson) - Algebra 2/Trigonometry 
  9. Quiz 2: The Unit Circle and Special Angles
  10. Reciprocal Functions
    • Secant (sec), cosecant (csc) and cotangent (cot) example 
  11. Points on the Terminal Side
    • Evaluating Trigonometric Functions for an Unknown Angle, Given a Point on the Angle, Ex 1 
  12.   Pythagorean Identities
    • Pythagorean trig identity from soh cah toa 
    • Using the Pythagorean trig identity 
  13. Quiz 3: The Reciprocal Functions and Identities
  14. Radian Measure
    • Introduction to radians 
    • Finding arc length from radian angle measure ​
    • Radian and degree conversion practice 
  15. Reference Angles   
    • Evaluating Trigonometric Functions Using the Reference Angle, Example 1 
  16. Velocity
    • Relationship between angular velocity and speed 
  17.  Quiz 4: Radian Measure
  18.  Review
  19.  Test
  20.  Alternate Test
  21.  Glossary and Credits
  1. Graphing and Amplitude
    • Midline, amplitude and period of a function 
    • Example: Graph, domain, and range of sine function 
  2. Project: The Reciprocal Functions: Complete the assignment as a part of this project.
  3. Period and Frequency
    • Precalculus - Find an Equation for the Sine or Cosine Wave 
    • Example: Amplitude and period 
  4. Vertical and Horizontal Translations
    • Example: Amplitude and period transformations 
  5. Sinusoidal Functions
    • Example: Graph, domain, and range of sine function 
    • Example: Graph of cosine 
  6. Quiz 1: Graphing
  7. Inverse Functions
    • Inverse trig functions: arcsin 
    • Inverse trig functions: arccos 
    • Inverse trig functions: arctan 
  8. Inverse Reciprocal Functions
    • Graphing Secant & Cosecant w/ t-table 
  9. Trigonometric Equations: Part I
    • Trigonometry - Solving Trigonometric Equations
  10. ​Trigonometric Equations: Part II
    • Precalculus - Trigonometric Equations that Require Factoring  
  11. Quiz 2: Inverse Trigonometric Functions
  12. Review
  13. Test
  14. Alternate Test
  15. Glossary and Credits

UNIT 3 - ANALYTIC TRIGONOMETRY
UNIT 4 - TRIGONOMETRIC APPLICATIONS
  1. The Fundamental Trigonometric Identities
    • Fundamental Trigonometric Identities: Reciprocal, Quotient, Pythagorean  
    • Examples using pythagorean identities to simplify trigonometric expressions 
    • Precalculus - Using Trigonometric Identities 
  2. Proving Identities
    • Verifying Trigonometric Identities: The Fundamental Identities
    • ​​Examples using pythagorean identities to simplify trigonometric expressions 
  3. Cosine Addition Formula
    • The Cosine Addition Formulas  
    • The Cosine Addition Formulas 
  4. Sine Addition Formula
    • The Sine Addition Formula   
    • Using the Sine and Cosine Addition Formulas To Prove Identities   
    • Sum and Difference Identities for Sine and Cosine, More Examples #1 
  5. Tangent Addition Formula
    • Sum and Difference Trigonometric Identities 
    • Sum and Difference Identities for Tangent  
  6.  Quiz 1: Identities and Addition Formulas
  7.  Double-Angle Formulas
    • Double angle formula for cosine example 
    • Trig: Double-Angle Formulas 
  8. Half-Angle Formulas
    • Precalculus - The Half-Angle Identities 
    • Trig: Half-Angle Formulas 
  9. Converting Between Products and Sums
    • Trigonometry - Sum-to-product Formulas - Example 1 
    • Trigonometry - Product-to-sum Formulas - Example 1 
  10.  Quiz 2: More Identities
  11.  Review
  12.  Test
  13.  Alternate Test
  14.  Glossary and Credits
  1. Law of Sines
    • Law of sines  
    • Law of sines for missing angle 
  2. Ambiguity and Area of a Triangle
    • Ambiguous Case Part 1 
    • Ambiguous Case Part 2  
    • Using Sine to Calculate the Area of a Triangle 
  3. Law of Cosines: Finding a Side
    • Law of cosines 
  4. Law of Cosines: Finding an Angle
    • Law of cosines to determine grade  
  5. Quiz 1: Trigonometry of Oblique Triangles
  6. Introduction to Vectors
    • Vector representations exercise example 
    • Introduction of Vectors  
    • Vector Applications  
    • Vector Operations  ​
  7. Vector Components   
    • Precalculus - The Angle Between Vectors  
    • Inclined plane force components   
    • Precalculus - The Resultant of Two Forces  
  8. Navigation Application
    • Precalculus - Navigation Problems 
  9. Vector Multiplication
    • Multiplying a vector by a scalar 
    • Subtracting vectors exercise example 
    • Vector dot product and vector length 
  10.  Quiz 2: Vectors
  11.  Review
  12.  Test
  13.  Alternate Test
  14.  Glossary and Credits

UNIT 5 - POLAR COORDINATES
​UNIT 6 - COURSE REVIEW AND EXAM
  1. ​Introduction to Polar Coordinates
    • Polar coordinates 1  
    • Polar coordinates  
  2. Polar Equations
    • Understanding Polar coordinates 
    • ​Understanding Polar coordinates
  3. Polar Curves
    • Precalculus - Graphing Polar Equations 
    • Precalculus - Families of Polar Curves: Circles, Cardiods, and Limacon 
  4. Polar Forms of Conics
    • Polar Form of a Conic: Finding the Type, the Directrix and Eccentricity   
    • Families of Polar Curves: Conic Sections 
  5. Quiz 1: Polar Equations
  6. Polar Form of Complex Numbers
    • Polar Form of a Conic: Finding the Type, the Directrix and Eccentricity 
  7. Multiply and Divide Complex Numbers
    • Multiplying complex numbers 
    • Dividing complex numbers 
  8. Powers and Nth Roots
    • DeMoivre's Theorem: Raising a Complex Number to a Power, Ex 1  
    • DeMoivre's Theorem: Raising a Complex Number to a Power, Ex 2 
    • Roots of Complex Numbers, Ex 1 
  9. Project: Fractals: Complete the assignment associated with this project. 
  10. Quiz 2: Complex Numbers
  11. Review
  12. Test
  13. Alternate Test
  14. Glossary and Credits
  1. Review
  2.  Exam
  3.  Alternate Exam
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