trigonometry academic library 

​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.

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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

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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

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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