Trigonometry
The subject of trigonometry is one of the most comprehensive and important parts of Mathematics 3. It is directly related to both geometry and functions. Because this subject has both visual and algebraic aspects, it can sometimes seem complex to students. Therefore, in order to present the subject in a more understandable, simple, and systematic way, we will examine it in two parts:
🔹 Part 1: We will focus on basic concepts, definitions, and trigonometric ratios related to triangles.
🔹 Part 2: We will emphasize more advanced formulas, graphical properties of functions, and trigonometric equations.
Thanks to this two-part structure, you will both solidify your foundations and more easily grasp advanced trigonometry topics.
Trigonometry Course Content
📘 Trigonometry – Part 1: Basic Concepts and Triangle Trigonometry
- Directed Angles: Defining angles as positive or negative based on their direction of rotation.
- Unit Circle: Visual representation of trigonometric ratios and the fundamental definition of functions.
- Angle Measurement Units: Conversions between degrees and radians.
- Wrapping Function: The wrapping motion on the unit circle according to the size of the angle.
- Reference Angle (Principal Value): The method for finding the primary value of an angle (between 0° and 360°).
- Trigonometric Functions: Definitions and values of sine, cosine, tangent, and cotangent.
- Trigonometric Ratios for 90° (π/2) and Larger Angles: Sign and value changes of functions across different quadrants.
- Trigonometric Ratios: Calculating trigonometric ratios in a right-angled triangle.
- Trigonometric Theorems in Triangles: The Law of Sines, Law of Cosines, and area formulas.
📗 Trigonometry – Part 2: Identities, Equations, and Graphs
- Sum and Difference Formulas: Formulas for \(\sin(a \pm b)\), \(\cos(a \pm b)\), and \(\tan(a \pm b)\).
- Double-Angle Formulas: Expressing trigonometric values based on half of the given angle.
- Product-to-Sum and Sum-to-Product Formulas: Formulas that convert sums into products and products into sums.
- Trigonometric Equations: Methods for solving equations containing trigonometric expressions.
- Periodic Functions: The repeating structure of trigonometric functions.
- Graphing Trigonometric Functions: Graphical properties of functions like sin, cos, and tan (period, amplitude, phase shift).
- Inverse Trigonometric Functions: Definitions and graphs of the inverse sine, inverse cosine, and inverse tangent functions.
Throughout this page, we will study trigonometry topics systematically, starting from scratch. Each heading will be presented on separate pages along with detailed explanations, sample question solutions, and visual supports.
We are making a solid introduction together to Trigonometry, one of the most enjoyable and powerful subjects of Mathematics 3. If you are ready, let’s begin!
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