Model with Trigonometric Functions

A comprehensive review suite for the New York State Mathematics Regents exams, including Algebra 1, Geometry, and Algebra 2, featuring mastery blueprints, calculator strategies, and exam-taking tips.

A 3-day healthcare-themed project for remedial precalculus students. It covers algebra 2 fundamentals, systems of equations, and introductory trigonometric transformations within clinical contexts.

A comprehensive prep sequence for the most challenging questions on the ACT Math and Science sections. It focuses on high-level conceptual blueprints for math topics like complex numbers and matrices, alongside speed-reading and data-interpretation strategies for the Science section.

A comprehensive ACT Math preparation program focusing on essential strategies, high-yield Algebra and Geometry concepts, and realistic practice to boost scores.

A targeted intervention sequence focused on mastering trigonometric equations through inverse functions, visual symmetry, and contextual application. This sequence provides Tier 2 support for students needing scaffolded paths to find both principal and secondary solutions.

This mathematical physics sequence explores the coordinate systems necessary for solving problems involving complex shapes, moving beyond Cartesian coordinates to General Curvilinear systems. Students derive scale factors, volume elements, and differential operators, culminating in solving Laplace's equation and understanding metric tensors.

A high school trigonometry sequence that uses the physics of sound waves to teach modeling with trigonometric functions. Students explore pitch as frequency, volume as amplitude, and the superposition of waves to create harmonies and digital tones.

A comprehensive unit on modeling real-world periodic phenomena using trigonometric functions across physics, biology, and astronomy. Students master identifying amplitude, midline, and period from contextual data to build and solve predictive equations.

A comprehensive unit where students act as data scientists to model real-world environmental phenomena using trigonometric functions. They progress from visual estimation to precise algebraic modeling and technological regression to predict future environmental conditions.

A 10th-grade trigonometry unit where students model circular motion using Ferris wheels, translating physical dimensions like radius, hub height, and speed into sine and cosine functions.

A comprehensive unit on trigonometric transformations, focusing on how parameters A, B, C, and D modify the parent sine and cosine functions. Students progress from simple vertical shifts to complex multi-parameter modeling.

An advanced 11th-grade Calculus unit focusing on the integration of parametric and polar coordinate systems. Students analyze motion, calculate complex areas, perform error analysis, and complete a final synthesis project based on particle kinematics.

A mini-lesson on graphing, analyzing, and modeling transformed sine and cosine trigonometric waves. Students learn to identify key parameters (amplitude, period, phase shift, midline) from equations and graphs, and apply them to periodic real-world scenarios.

A mini-lesson on transforming trigonometric sine and cosine functions. Students will learn to identify key wave parameters, sketch transformations on a grid, write equations from sinusoidal graphs, and model real-world periodic phenomena.

A high-intensity review session for AP Precalculus Unit 3, covering trigonometric functions, inverse functions, and polar coordinates through a "Radar Tech" thematic lens.

A comprehensive review for Unit 3 of AP Precalculus, focusing on trigonometric and polar functions through reference materials and practice assessments.

A comprehensive lesson on graphing Sine and Cosine functions, featuring guided notes, instructional slides, and a detailed answer key. Students will learn to identify amplitude, period, midline, and phase shifts to accurately sketch periodic graphs.

A targeted intervention lesson for high school students focused on solving trigonometric equations using inverse functions. This lesson uses a scaffolded 'blueprint' approach to help students navigate calculator settings, step-by-step equation solving, and interpreting results in real-world modeling contexts.

A Tier 2 small group intervention focused on identifying and modeling periodic parameters (amplitude, midline, and period) from graphs to build trigonometric equations. Students progress from visual identification to algebraic representation using a scaffolded approach.

A Tier 2 small group intervention lesson focused on modeling real-world periodic phenomena using trigonometric functions. Students will learn to translate data from tables and graphs into sinusoidal equations, specifically targeting Colorado standard HS.F-TF.B.5.

A Tier 2 intervention lesson focused on modeling periodic phenomena using trigonometric functions. Students learn to extract amplitude, midline, and frequency from real-world data to construct sine and cosine equations.

A high school mathematics lesson connecting real-world periodic patterns in sound and tides to trigonometric identities, specifically horizontal shifts by multiples of the period.

A lesson for Advanced Precalculus students focusing on expressing vectors as linear combinations of the unit vectors i and j, featuring physics-based force problems and rapid-fire conversion practice.

Students will learn to derive sine and cosine equations from periodic graphs, focusing on the strategic choice between functions based on phase shifts and key points. This lesson uses a high-quality video walkthrough and collaborative discussion to master the a, b, c, and d transformations.