Скачать или смотреть Calculus-ITU-2024 | Lecture 4 |Trigonometry and Exponential Growth in Calculus

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*Time Stamps*:
00:00 - Sine and the Unit Circle : Delve into the beautiful world of sine waves, exploring their connection to right triangles and the unit circle. Learn how sine values correspond to angles, and uncover the mysteries behind the magic number: 90 degrees.

08:13 - Triangle Geometry : See how sine and cosine bring triangles to life, transforming abstract angles into tangible side lengths. Experience firsthand how these trigonometric ratios evolve as angles shift, and understand why visualization is key to mastering these relationships.

16:18 - Angle Representation and Sliders : Ever wondered how changing an angle looks in real-time? We use interactive sliders to visually represent angles and their impact on sine and cosine, making abstract concepts intuitive and engaging.

24:26 - Radians and Arc Length : Learn the art of radians—an essential unit of measure in calculus—and discover how they connect directly to arc length. Through hands-on examples, we'll make the leap from degrees to radians effortless and meaningful.

32:30 - Animating Functions : Want to see math in motion? We explore how changing animation speeds can turn circles into ellipses and how manipulating parameters alters the shapes and dynamics of your graphs. Perfect for visual learners looking to make calculus come alive.

40:42 - Exploring Exponential Functions : Transitioning from trigonometry to calculus, we embark on a journey through exponential growth, contrasting it with polynomial functions. Witness the explosive power of exponential functions and why they outgrow polynomials as x increases.

48:45 - Exponential vs Polynomial Growth : With the help of real-world examples, discover the faster-than-light growth of exponential functions compared to their polynomial cousins. Learn how derivatives offer insights into their behavior and growth rates.