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Unit 3: Trigonometric and Polar Functions
3.1 Periodic Phenomena
3.2 Sine, Cosine, and Tangent
3.3 Sine and Cosine Function Values
3.4 Sine and Cosine Function Graphs
3.5 Sinusoidal Functions
3.6 Sinusoidal Function Transformations
3.7 Sinusoidal Function Context and Data Modeling
3.8 The Tangent Function
3.9 Inverse Trigonometric Functions
3.10 Trigonometric Equations and Inequalities
3.11 The Secant, Cosecant, and Cotangent Functions
3.12 Equivalent Representations of Trigonometric Functions
3.13 Trigonometry and Polar Coordinates
3.14 Polar Function Graphs
3.15 Rates of Change in Polar Functions
In this video, I thoroughly describe and reteach the main components of the sections listed above found in the official College Board AP Precalculus course description found at https://apcentral.collegeboard.org/media/pdf/ap-precalculus-course-and-exam-description.pdf. Afterwords, I provide multiple examples and give descriptive solutions to AP Precalculus-style problems. Topics in this video include…
3.1 Periodic Phenomena: Study of events or processes that repeat in a predictable pattern over time.
3.2 Sine, Cosine, and Tangent: Fundamental trigonometric functions defined as ratios of sides in a right triangle.
3.3 Sine and Cosine Function Values: Understanding the values of sine and cosine functions for various angles.
3.4 Sine and Cosine Function Graphs: Graphing the sine and cosine functions to visualize their periodic behavior.
3.5 Sinusoidal Functions: Functions that can be modeled by sine or cosine functions, characterized by periodic oscillations.
3.6 Sinusoidal Function Transformations: Modifying sinusoidal functions by transformations such as translations, reflections, and dilations.
3.7 Sinusoidal Function Context and Data Modeling: Applying sinusoidal functions to real-world situations and modeling periodic data.
3.8 The Tangent Function: Trigonometric function defined as the ratio of sine to cosine, commonly used in geometry and calculus.
3.9 Inverse Trigonometric Functions: Functions that "undo" the actions of trigonometric functions, allowing us to find angles given trigonometric ratios.
3.10 Trigonometric Equations and Inequalities: Solving equations and inequalities involving trigonometric functions.
3.11 The Secant, Cosecant, and Cotangent Functions: Reciprocal trigonometric functions defined as ratios involving cosine, sine, and tangent.
3.12 Equivalent Representations of Trigonometric Functions: Expressing trigonometric functions in terms of other trigonometric functions using various identities.
3.13 Trigonometry and Polar Coordinates: Studying trigonometric functions in the context of polar coordinates.
3.14 Polar Function Graphs: Graphing functions represented in polar coordinates.
3.15 Rates of Change in Polar Functions: Analyzing the rates of change of functions represented in polar coordinates, involving derivatives and understanding motion in polar contexts.
These topics are fundamental in precalculus and serve as a foundation for more advanced mathematical concepts.
These concepts are fundamental in precalculus and serve as building blocks for more advanced mathematical topics.
I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out: https://youtube.com/c/NickPerich
Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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