Trigonometric Graphs & Transformations | Trigonometry | Class 17 | AS Level P1 9709 | MathvsArham

Class #17 | Mastering Trigonometric Graphs & Transformations | AS 9709 P1 Welcome back to our AS Level Pure Mathematics 1 (9709) series! 🚀 In this seventeenth session, we move into the visual world of Trigonometry. We break down the characteristic shapes of Sine, Cosine, and Tangent curves and explore how they behave over different intervals. More importantly, we master the "Art of the Sketch"—learning how to transform these basic waves through stretches, reflections, and translations. Please note: This video is a recording of a live class session with Sir Arham Ahmed. This video covers: The "Big Three" Curves: Detailed analysis of the Sin(x), Cos(x), and Tan(x) graphs. Understanding Periods: Why Sin and Cos repeat every 360 degrees (2π) while Tan repeats every 180 degrees (π). The Tangent Mystery: Explaining Asymptotes—those "invisible walls" at 90 and 270 degrees where the Tan function simply cannot exist. Graph Transformations: How to modify your graph based on the equation y = a sin(bx) + c: Amplitude (a): The vertical stretch. Period Change (b): The horizontal stretch/compression. Vertical Shift (c): Moving the entire wave up or down. Step-by-Step Plotting: A foolproof 5-step method to sketch any transformed trig function accurately in your exam booklet. Worked Examples: Solving practice questions that ask you to "State the number of solutions" by looking at where two graphs intersect. By the end of this class, you won't just be drawing curves; you'll be reading them. You'll understand exactly how changing a single number in an equation flips, stretches, or moves the entire graph! Meet the Instructor Sir Arham Ahmed is an experienced, Cambridge-qualified Mathematics specialist. He focuses on high-energy, high-impact learning to help you win the "Math vs You" challenge and achieve your target grade in AS Level Mathematics. Don’t forget to like, subscribe, and hit the bell icon to stay updated with our P1 journey!