​Trigonometry is a five-unit elective 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

Need some extra help! We have it for you...any time you are ready.

Multiple ways for help in math no matter where you are learning…traditional classroom or distance education…review your material curriculum materials carefully, communicate with your teacher that you need more help, or in today’s digital world use videos of others who show students how to understand and complete their work as they watch and learn.  You have all three at NFC Academy.  Here are your videos for. Trigonometry.  ​​​

---

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 
2. Polar Equations
   • Polar coordinates 3 
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