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trigonometry

high school math honors course - one semester .5 credit
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​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.  
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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

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
OUR MISSION 
Using innovative technology together with successful educational practices and a biblical worldview curriculum in a distance educational environment to equip students for their future while serving and glorifying God. 

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NFC ACADEMY STATEMENT OF NON-DISCRIMINATION
NFC Academy admits students of any race, color, national and ethnic origin to all the rights, privileges, programs, and activities generally accorded or made available to students at the school. It does not discriminate on the basis of race, color, national or ethnic origin in the administration of its educational policies, admission policies, scholarship and loan programs and athletic or other school administered programs. 
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ETHICS IN EDUCATION STATEMENT
In accordance with the Florida Ethics in Education Act, all employees of NFC Academy have a duty to report all suspected or actual cases of child abuse, abandonment, or neglect. They have immunity from liability if they report such cases in good faith and have a duty to comply with child protective investigations. There is a legal penalty for not reporting suspected or alleged child abuse or alleged misconduct by instructional personnel or school administrators. The Florida Abuse Hotline is 1.800.962.2873. The NFC Academy contact is the Administrator’s Office – 850.385.7186 ext. 139

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