Learn to master trigonometric functions and their graphical representations through a comprehensive video series that covers fundamental concepts, graph transformations, and practical applications. Explore the basic properties of sine, cosine, and tangent functions, including their periods, amplitudes, and key features. Discover how to modify trigonometric graphs through frequency changes, amplitude adjustments, vertical and horizontal shifts, and reflections. Practice graphing complex trigonometric functions with multiple transformations and understand phase shift concepts through algebraic manipulation and visual examples. Work through real-world modeling problems such as Ferris wheel motion to see how trigonometric functions apply to practical situations. Develop skills in solving trigonometric equations using various methods including the Pythagorean identity and graphical approaches. Address common misconceptions and flawed reasoning in trigonometric identities while building a solid foundation for advanced mathematical concepts. Gain experience with exam-style questions involving domain restrictions, function intersections, and complex trigonometric expressions through step-by-step problem-solving demonstrations.

Syllabus

sin(x) + cos(x) = 1 by Identities (Flaw Explanation 1 of 2)
sin(x) + cos(x) = 1 by Identities (Flaw Explanation 2 of 2)
sin(x) + cos(x) = 1 by Identities (Flawed)
Tricky Trig Graph Question: Derivative
Tricky Trig Graph Question: Features & Sketching
Graphing Trigonometric Functions
Understanding Phase Shift with Trigonometric Functions (1 of 3: Simple Example)
Understanding Phase Shift with Trigonometric Functions (2 of 3: Reflecting Across Different Axes)
Understanding Phase Shift with Trigonometric Functions (3 of 3: Using Algebraic Manipulation)
Maths Test Review (2 of 2: Finding the solution of a trigonometric function)
Modifications of Trigonometric Graphs (1 of 5: Frequency/Period)
Modifications of Trigonometric Graphs (2 of 5: Amplitude)
Modifications of Trigonometric Graphs (3 of 5: Vertical Shift)
Modifications of Trigonometric Graphs (4 of 5: Horizontal Shift)
Modifications of Trigonometric Graphs (5 of 5: Reflection)
Modifying the Trigonometric Functions (Using live graphs)
Graphing y = tan(x÷3)
Trigonometric Graphs with Multiple Modifications (1 of 2: Phase & Frequency)
Trigonometric Graphs with Multiple Modifications (2 of 2: Amplitude & Vertical Shift)
Graphing Trigonometric Functions (Example: y = 3cos(x) - 2)
Reviewing Trigonometric Functions (1 of 3: Re-introducing the sine graph)
Reviewing Trigonometric Functions (2 of 3: Features of sine and cosine)
Reviewing Trigonometric Functions (3 of 3: Basic features of the tan graph)
The Ferris Wheel - Trigonometric Function Model (1 of 3: Setting up the equation)
The Ferris Wheel - Trigonometric Function Model (2 of 3: Adjusting the period)
The Ferris Wheel - Trigonometric Function Model (3 of 3: Interpreting results)
Trigonometric Graph Exam Question (1 of 2: Sketching the functions)
Trigonometric Graph Exam Question (2 of 2: Domain for intersections)
Solving Trigonometric Equations (3 of 3: Shifted and dilated function)
Solving Trigonometric Equations (2 of 3: Using the graph)
Solving Trigonometric Equations (1 of 3: Using the Pythagorean Identity)