Right triangle ratios, unit circle definitions, and fundamental identities applied to angles and geometric relationships. Models periodic phenomena using trigonometric functions to analyze real-world cycles and waveforms.
A high school trigonometry lesson focusing on the critical step of quadrant analysis in half-angle identities, ensuring students choose the correct sign for trigonometric outputs.
A high-level trigonometry lesson for Honors Pre-Calculus students focusing on verifying complex identities using double-angle and half-angle formulas. Students will engage in quadrant analysis and tactical formula selection through a hands-on identity reconstruction activity.
Students derive double-angle identities from sum formulas and use Pythagorean identities to prove alternate forms of the cosine double-angle identity.
Students will master the use of half-angle identities to determine exact trigonometric values for non-standard angles. The lesson includes a video-guided derivation and a collaborative challenge where students verify their exact radicals against decimal approximations.
A high-school trigonometry lesson focused on double-angle and half-angle identities. Students watch a comprehensive review video and design a 'cheat sheet' with built-in warnings for common algebraic traps.
A 10th-grade geometry lesson exploring the co-function relationship between sine and cosine using right triangles and complementary angles. Students analyze a video, complete a comparison table, and conduct a hands-on verification activity.
Students will master the 'Left-Hand Technique' for sine and cosine before extending the logic to derive a new finger-based formula for tangent values.
Students will master the evaluation of composite inverse trigonometric functions, specifically learning how to identify when function 'cancellation' is valid and when restricted range adjustments are required.
Students will explore how the labels 'Opposite' and 'Adjacent' are relative to the chosen reference angle. Through a video demonstration and a collaborative partner activity, they will discover the relationship between the trigonometric ratios of complementary angles.
Students will synthesize periodic, reciprocal, cofunction, and even-odd identities to solve complex trigonometric problems. This lesson includes a fast-paced identity matching warm-up, a guided video analysis, and a collaborative three-stage relay race activity.
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.
Students discover the cofunction relationships between sine and cosine through a combination of calculator exploration and geometric proofs using right triangles. The lesson emphasizes the concept of complementary angles and the etymology of trigonometric terms.
A comprehensive lesson where students build a trigonometric identity toolkit using horizontal shifts, complementary angles, and symmetry. Includes video-guided instruction and a formal reference sheet creation activity.
Students use graphing technology and algebraic proofs to categorize trigonometric and composite functions as even, odd, or neither, focusing on the symmetry of the unit circle.
An intensive lesson for 11th-12th grade students focused on mastering trigonometric ratios, the ASTC quadrant rule, and fundamental identities to simplify expressions and solve ACT-style math problems.
A trigonometry lesson focused on calculating the area of a triangle using the SAS sine formula, including a video analysis of the relationship between the sine rule and the standard area formula.
This lesson bridges the gap between right-triangle trigonometry and coordinate geometry. Students explore the unit circle as a tool for defining sine, cosine, and tangent as (x, y) coordinates, culminating in an activity that proves these ratios remain constant regardless of the circle's radius.
A high-energy review lesson for high school math students focusing on the synthesis of the Pythagorean theorem, triples, and trigonometry. Students engage in a competitive 'Trig Relay' to master multi-step geometric problem solving.
A high school Pre-Calculus lesson focused on the power of variable substitution to solve non-standard quadratic equations, including fractional indices and trigonometric forms.
Students identify and solve equations with a quadratic structure across various contexts (trigonometry, logarithms, and exponents) using the substitution method.
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 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.
Students will apply their knowledge of trigonometric transformations to model the movement of a Ferris wheel. They will identify key parameters (amplitude, midline, period, phase shift) from real-world data and construct periodic equations.
An undergraduate-level exploration into the behavior of transcendental functions at infinity, focusing on the distinction between unbounded growth and oscillatory non-existence. Students will analyze sine waves, exponentials, and damped oscillations to master formal limit notation and end-behavior analysis.
A high school math lesson that connects abstract precalculus concepts to real-world engineering and science applications using video analysis and group research.
A 10th-grade math lesson focused on identifying transcendental equations that require numerical approximation versus standard algebraic isolation, featuring a 'Mad Scientist' lab theme for creating 'Frankenstein Equations'.
An advanced introduction to the metric tensor and non-Euclidean geometry, serving as a primer for General Relativity.
Students solve Laplace's equation for systems with spherical symmetry, introducing Legendre polynomials and Spherical Harmonics.
Students translate the Del operator into general curvilinear coordinates and apply these operators to physical vector fields.
Focusing on integration, students construct volume and area elements (Jacobians) for spherical and cylindrical geometries and practice integrating scalar fields over complex 3D domains.
Students derive basis vectors and scale factors for general orthogonal curvilinear coordinates and learn how to define position vectors in non-Cartesian geometries.
As a final project, students use their knowledge of frequencies, amplitude, and domain restrictions to 'program' a digital ringtone using a graphing calculator or synthesizer software.
Students explore the concept of superposition by adding trigonometric functions together, visualizing how chords and 'beats' (interference) are represented mathematically.
This lesson focuses on amplitude as the mathematical representation of volume, exploring how changes in coefficient affect the intensity of a sound wave without changing its pitch.
Students define the mathematical relationship between musical pitch (Hertz) and the period of a sine function, learning to write equations that represent specific musical notes.
In this introductory lesson, students use real-time oscilloscope software to visualize their own voices and musical instruments as trigonometric waveforms, identifying the periodic nature of sound.
Students use their constructed models to extrapolate and answer questions about future events, solving trigonometric inequalities graphically.
Students use graphing calculators or regression software to fit trigonometric equations to data sets. They compare their hand-calculated models to the regression models.
A comprehensive ACT Math preparation module focusing on core concepts, time management strategies, and targeted practice across all test categories.
A comprehensive 20-question practice test and answer key designed to prepare students for the TSIA2 Mathematics assessment, focusing on algebraic, geometric, and statistical reasoning.
In this lesson, students bridge the gap between abstract Greek geometry and Renaissance physics by applying quadratic equations to projectile motion. Students watch a comprehensive breakdown of the kinematic-quadratic relationship, participate in historical-mathematical discussions, and design a catapult model that they must describe through theoretical algebraic modeling.
Students investigate how regular polygons with increasing numbers of sides eventually 'converge' into a circle, using the apothem formula to derive the area of a circle.
A discovery-based lesson where students use the Pythagorean Theorem to uncover the side ratios of 45-45-90 triangles, confirm their findings with a video, and build fluency through a 'Rapid Fire' practice session.
A lesson focused on 3D trigonometry where students derive the space diagonal of a cube and use trigonometric ratios to find the constant angle of elevation, regardless of the cube's side length.
A comprehensive lesson introducing students to sine, cosine, and tangent ratios through visual instruction, guided practice, and hands-on station rotations. Students will master the SOH CAH TOA mnemonic and apply it to various right triangles.
A foundational geometry lesson where students learn to identify right triangle sides (hypotenuse, opposite, adjacent) based on a specific reference angle using a 'Point of View' approach.
A high-energy math lesson where students master trigonometric ratios through the 'Legend of SOH CAH TOA' creative project, transforming abstract mnemonics into memorable visual stories.
A 10th-grade advanced math lesson focused on the difference between standard trigonometric angles and navigational bearings, featuring vector addition applications.
A high school mathematics lesson focused on applying vector addition and bearing calculations to real-world navigation scenarios, specifically airplanes and watercraft.
A high-energy geometry lesson where students act as geometric investigators to solve complex rhombus problems using properties, Pythagorean theorem, and area formulas. The lesson includes a 'mystery case' collaborative activity and explores 'identity' solutions in algebra.
A 10th-grade Geometry lesson focused on identifying, defining, and sketching angles of elevation and depression from real-world scenarios. Includes video analysis, a collaborative diagram-drawing relay, and error-correction practice.
A high school geometry lesson where students act as ADA compliance architects, using inverse tangent functions to calculate ramp angles and ensure they meet accessibility standards.
A high school geometry lesson focused on using the tangent ratio and clinometers to solve real-world height problems through an 'Indirect Measurement Lab'.
Students master trigonometric word problems by analyzing real-world scenarios, watching a guided tutorial, and designing their own 'Angle Architecture' posters. The lesson focuses on correctly identifying angles of elevation and depression and applying SOH CAH TOA.
A 10th-grade Honors Geometry lesson connecting trigonometric ratios to special right triangles through word problems and exact values. Students analyze a video segment on special right triangles and solve a series of word problems requiring answers in simplest radical form.
Students will investigate the property that similar right triangles share constant trigonometric ratios by measuring three differently sized similar triangles and calculating their sine, cosine, and tangent values.
A high school geometry lesson teaching the Left-Hand Technique to quickly derive sine and cosine values for first-quadrant special angles (30, 45, and 60 degrees). Students compare this physical mnemonic to traditional triangle-based derivation for speed and accuracy.
Students will master the 'Left-Hand Technique' for first-quadrant trigonometric values through a kinesthetic, hands-on activity. By creating a physical 'Glove of Knowledge' or hand-traced guide, students will internalize the pattern of square roots and finger counting for sine and cosine.
Students will master the Left-Hand Technique for 1st-quadrant trigonometric values, moving from basic finger setup to rapid mental calculation of complex expressions through a competitive tournament.
A 10th-grade math lesson that introduces the Left-Hand Technique for memorizing trig values of special angles, focusing on pattern recognition and the mathematical logic behind the shortcut.
A high school trigonometry lesson on converting between Degrees, Minutes, Seconds (DMS) and Decimal Degrees, using the 'Time vs. Space' analogy. Students learn the sexagesimal system through video examples and a collaborative calculator relay activity.
A high school Pre-Calculus lesson focused on the precision of converting between Decimal Degrees and Degrees, Minutes, Seconds (DMS), featuring an 'Error Analysis Lab' to investigate the mathematical impact of rounding.
A 10th-grade math lesson focused on converting Decimal Degrees to Degrees, Minutes, and Seconds (DMS) through algorithmic thinking and pseudo-coding. Students will watch an instructional video, map out flowcharts, and write logic for a conversion script.
Students will master evaluating inverse trigonometric functions (arcsin, arccos, arctan) using the unit circle by understanding domain and range restrictions. The lesson includes a 'forbidden quadrant' activity to visualize why certain angles are excluded from the range of inverse functions.
In this Precalculus lesson, students investigate why trigonometric functions require domain restrictions to be invertible. Using a medical surgery theme, students 'perform surgery' on sine, cosine, and tangent graphs to isolate the standard restricted intervals used for inverse functions.
A high school math lesson focused on identifying valid and undefined inputs for inverse trigonometric functions, distinguishing between domain and range restrictions through calculator exploration and error analysis.
A comprehensive lesson for AP Calculus Prep/Honors Precalculus on graphing inverse trigonometric functions. Students explore the necessity of domain restrictions and use 'Patty Paper' (tracing paper) to physically visualize the reflection of restricted trig graphs over the line y=x.
A high-level mathematics lesson focused on defining restricted domains for non-invertible functions to create valid inverse functions, preparing students for calculus and inverse trigonometry.
A high-energy Algebra 2 lesson where students identify function transformations through a rapid-fire video review and create original geometric art using parent functions.
A high school Pre-Calculus lesson focused on distinguishing between horizontal and vertical scaling through coordinate analysis and invariant points. Students analyze absolute value and sine transformations to understand how specific points remain fixed under different scaling types.
