academic instructional library

​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
​​NFC Academy works diligently to provide additional materials to our homeschool students which will help bridge the gap from a traditional classroom to the home with a teacher who does not have direct daily live interaction with the student.  These supplementary videos which are typically from Kahn Academy or available through research in YouTube are screened prior to being included.  However, material offered over the Internet, especially using YouTube may change without notice to the user.  We recommend screening of such material by the home to avoid content that may be unacceptable in an advertising promotion which could be added as a part of some videos.
UNIT 1 - RIGHT TRIANGLE TRIGONOMETRY
UNIT 2 - GRAPHING AND INVERSE FUNCTIONS
  1. Course Overview
  2. Lengths of Sides
  3. Angle Measures
  4. Indirect Measure
  5. Quiz 1: Solving a Right Triangle
  6. Angles in the Coordinate Plane
  7. The Unit Circle
  8. Trigonometric Values of Special Angles
  9. Quiz 2: The Unit Circle and Special Angles
  10. Reciprocal Functions
  11. Points on the Terminal Side
  12.   Pythagorean Identities
  13. Quiz 3: The Reciprocal Functions and Identities
  14. Radian Measure
  15. Reference Angles   
  16. Velocity
  17.  Quiz 4: Radian Measure
  18.  Review
  19.  Test
  20.  Alternate Test
  21.  Glossary and Credits
  1. Graphing and Amplitude
  2. Project: The Reciprocal Functions: Complete the assignment as a part of this project.
  3. Period and Frequency
  4. Vertical and Horizontal Translations
  5. Sinusoidal Functions
  6. Quiz 1: Graphing
  7. Inverse Functions
  8. Inverse Reciprocal Functions
  9. Trigonometric Equations: Part I
  10. ​Trigonometric Equations: Part II
  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
  2. Proving Identities
    1. ​Examples using pythagorean identities to simplify trigonometric expressions 
  3. Cosine Addition Formula
  4. Sine Addition Formula
  5. Tangent Addition Formula
  6.  Quiz 1: Identities and Addition Formulas
  7.  Double-Angle Formulas
  8. Half-Angle Formulas
  9. Converting Between Products and Sums
  10.  Quiz 2: More Identities
  11.  Review
  12.  Test
  13.  Alternate Test
  14.  Glossary and Credits
  1. Law of Sines
  2. Ambiguity and Area of a Triangle
  3. Law of Cosines: Finding a Side
  4. Law of Cosines: Finding an Angle
  5. Quiz 1: Trigonometry of Oblique Triangles
  6. Introduction to Vectors
  7. Vector Components   
  8. Navigation Application
  9. Vector Multiplication
  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
  2. Polar Equations
  3. Polar Curves
  4. Polar Forms of Conics
  5. Quiz 1: Polar Equations
  6. Polar Form of Complex Numbers
  7. Multiply and Divide Complex Numbers
  8. Powers and Nth Roots
  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