TRIGONOMETRY ACADEMIC LIBRARY

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Trigonometry Online

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.

The math academic libraries are not considered as a replacement for the online curriculum, the media presentations, and instruction with daily lessons which must be completed including daily quizzes and unit tests or help from your teacher, but a supplement to the curriculum for additional practice and instruction available 24/7.

Admission

Trigonometry Online

UNIT 1 – RIGHT TRIANGLE TRIGONOMETRY

Course Overview
Lengths of Sides
- Basic Trigonometry
- Introduction to Trigonometric Functions Using Triangles
Angle Measures
- Introduction to Inverse Trigonometric Functions
- Introduction to Inverse Sine, Inverse Cosine, Inverse Tangent
Indirect Measure
- Angle of Elevation and Depression
- Indirect Measurement Using Similar Triangles
Quiz 1: Solving a Right Triangle
Angles in the Coordinate Plane
- Coterminal Angles – Example 1
The Unit Circle
- Introduction to the unit circle
Trigonometric Values of Special Angles
- Evaluating Sine, Cosine and Tangent at 30, 45, and 60 Degrees (mini lesson) – Algebra 2/Trigonometry
Quiz 2: The Unit Circle and Special Angles
Reciprocal Functions
- Secant (sec), cosecant (csc) and cotangent (cot) example
Points on the Terminal Side
- Evaluating Trigonometric Functions for an Unknown Angle, Given a Point on the Angle, Ex 1
Pythagorean Identities
- Pythagorean trig identity from soh cah toa
- Using the Pythagorean trig identity
Quiz 3: The Reciprocal Functions and Identities
Radian Measure
- Introduction to radians
- Finding arc length from radian angle measure
- Radian and degree conversion practice
Reference Angles
- Evaluating Trigonometric Functions Using the Reference Angle, Example 1
Velocity
- Relationship between angular velocity and speed
Quiz 4: Radian Measure
Review
Test
Alternate Test
Glossary and Credits

UNIT 2 – GRAPHING AND INVERSE FUNCTIONS

Graphing and Amplitude
- Midline, amplitude and period of a function
- Example: Graph, domain, and range of sine function
Project: The Reciprocal Functions:Complete the assignment as a part of this project.
Period and Frequency
- Precalculus – Find an Equation for the Sine or Cosine Wave
- Example: Amplitude and period
Vertical and Horizontal Translations
- Example: Amplitude and period transformations
Sinusoidal Functions
- Example: Graph, domain, and range of sine function
- Example: Graph of cosine
Quiz 1: Graphing
Inverse Functions
Inverse Reciprocal Functions
- Graphing Secant & Cosecant w/ t-table
Trigonometric Equations: Part I
- Trigonometry – Solving Trigonometric Equations
Trigonometric Equations: Part II
- Precalculus – Trigonometric Equations that Require Factoring
Quiz 2: Inverse Trigonometric Functions
Review
Test
Alternate Test
Glossary and Credits

UNIT 3 – ANALYTIC TRIGONOMETRY

The Fundamental Trigonometric Identities
Proving Identities
- Verifying Trigonometric Identities: The Fundamental Identities
- Examples using pythagorean identities to simplify trigonometric expressions
Cosine Addition Formula
- The Cosine Addition Formulas
- The Cosine Addition Formulas
Sine Addition Formula
Tangent Addition Formula
- Sum and Difference Trigonometric Identities
- Sum and Difference Identities for Tangent
Quiz 1: Identities and Addition Formulas
Double-Angle Formulas
- Double angle formula for cosine example
- Trig: Double-Angle Formulas
Half-Angle Formulas
- Precalculus – The Half-Angle Identities
- Trig: Half-Angle Formulas
Converting Between Products and Sums
- Trigonometry – Sum-to-product Formulas – Example 1
- Trigonometry – Product-to-sum Formulas – Example 1
Quiz 2: More Identities
Review
Test
Alternate Test
Glossary and Credits

UNIT 4 – TRIGONOMETRIC APPLICATIONS

Law of Sines
- Law of sines
- Law of sines for missing angle
Ambiguity and Area of a Triangle
Law of Cosines: Finding a Side
- Law of cosines
Law of Cosines: Finding an Angle
- Law of cosines to determine grade
Quiz 1: Trigonometry of Oblique Triangles
Introduction to Vectors
Vector Components
Navigation Application
- Precalculus – Navigation Problems
Vector Multiplication
Quiz 2: Vectors
Review
Test
Alternate Test
Glossary and Credits

UNIT 5 – POLAR COORDINATES

Introduction to Polar Coordinates
- Polar coordinates 1
- Polar coordinates
Polar Equations
- Understanding Polar coordinates
- Understanding Polar coordinates
Polar Curves
- Precalculus – Graphing Polar Equations
- Precalculus – Families of Polar Curves: Circles, Cardiods, and Limacon
Polar Forms of Conics
- Polar Form of a Conic: Finding the Type, the Directrix and Eccentricity
- Families of Polar Curves: Conic Sections
Quiz 1: Polar Equations
Polar Form of Complex Numbers
- Polar Form of a Conic: Finding the Type, the Directrix and Eccentricity
Multiply and Divide Complex Numbers
- Multiplying complex numbers
- Dividing complex numbers
Powers and Nth Roots
Project: Fractals: Complete the assignment associated with this project.
Quiz 2: Complex Numbers
Review
Test
Alternate Test
Glossary and Credits

UNIT 6 – COURSE REVIEW AND EXAM

Review
Exam
Alternate Exam