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  • CCSS.Math.Content.HSF-TF.B.5 - Choose trigonometric functions to model periodic phenomena with specif...
  • CCSS.Math.Content.HSF-TF.B.5 - Choose trigonometric functions to model periodic phenomena with specif...
Algebra II Module 2
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Module 2 builds on students' previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Algebra
Mathematics
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
08/15/2014
Foxes and Rabbits 2
Unrestricted Use
CC BY
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The example of rabbits and foxes was introduced in the task (8-F Foxes and Rabbits) to illustrate two functions of time given in a table. We are now in a position to actually model the data given previously with trigonometric functions and investigate the behavior of this predator-prey situation.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/29/2012
Foxes and Rabbits 3
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The example of rabbits and foxes was introduced in 8-F Foxes and Rabbits to illustrate two functions of time given in a table. The same situation was used in F-TF Foxes and Rabbits 2 to find trigonometric functions modeling the data in the table. The previous situation was somewhat unrealistic since we were able to find functions that fit the data perfectly. In this task, on the other hand, we do some legitimate modelling, in that we come up with functions that approximate the data well, but do not perfectly match, the given data.

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
08/30/2012
Fundamentals of Waves
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This lesson is broken up into three different parts.Part 1/Resource 1In this lesson students will learn the basics of waves and how to graph them.  They will learn how to find the period, amplitude, and frequency of a wave. Part 2/Resource 2In this lesson students learn the connection between waves and music. Part 3/ Resource 3Students will learn the concept of superposition. CC-BY Kaleb Alles, Mountain Heights Academy 

Subject:
Trigonometry
Material Type:
Lesson Plan
Author:
Crystal Van Ausdal
Date Added:
04/17/2018
If As the Wheel Turns
Unrestricted Use
CC BY
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In this task, students use trigonometric functions to model the movement of a point around a wheel and, in the case of part (c), through space (F-TF.5). Students also interpret features of graphs in terms of the given real-world context (F-IF.4).

Subject:
Functions
Mathematics
Material Type:
Activity/Lab
Provider:
Illustrative Mathematics
Provider Set:
Illustrative Mathematics
Author:
Illustrative Mathematics
Date Added:
05/01/2012
MOWWM Unit 6: The Arts Topic 1 - Catch a Wave with Music
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Modeling Our World with Mathematics Unit 6: The Arts Topic 1 - Catch a Wave with Music

Subject:
Mathematics
Material Type:
Module
Author:
Hannah Hynes-Petty
Washington OSPI OER Project
Washington OSPI Mathematics Department
Arlene Crum
Date Added:
10/13/2020
Measuring Distance with Sound Waves
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Educational Use
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Students learn about sound waves and use them to measure distances between objects. They explore how engineers incorporate ultrasound waves into medical sonogram devices and ocean sonar equipment. Students learn about properties, sources and applications of three types of sound waves, known as the infra-, audible- and ultra-sound frequency ranges. They use ultrasound waves to measure distances and understand how ultrasonic sensors are engineered.

Subject:
Applied Science
Engineering
Physical Science
Physics
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Irina Igel
Date Added:
09/18/2014
Seismic Waves: How Earthquakes Move the Earth
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Educational Use
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Students learn about the types of seismic waves produced by earthquakes and how they move the Earth. The dangers of earthquakes are presented as well as the necessity for engineers to design structures for earthquake-prone areas that are able to withstand the forces of seismic waves. Students learn how engineers build shake tables that simulate the ground motions of the Earth caused by seismic waves in order to test the seismic performance of buildings.

Subject:
Applied Science
Engineering
Geology
Physical Science
Material Type:
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Carleigh Samson
Denise W. Carlson
Stephanie Rivale
Date Added:
09/18/2014
Álgebra II Módulo 2
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CC BY-NC-SA
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(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

El módulo 2 se basa en el trabajo previo de los estudiantes con unidades y con funciones del álgebra I, y con relaciones y círculos trigonométricos de la geometría de la escuela secundaria. El corazón del módulo es el estudio de definiciones precisas de seno y coseno (así como tangente y las cofunciones) utilizando geometría transformacional de la geometría de la escuela secundaria. Esta precisión lleva a una discusión de una unidad matemáticamente natural de medida rotacional, un radian, y los estudiantes comienzan a desarrollar fluidez con los valores de las funciones trigonométricas en términos de radianes. Los estudiantes grafican funciones trigonométricas sinusoidales y otras, y usan los gráficos para ayudar a modelar y descubrir propiedades de las funciones trigonométricas. El estudio de las propiedades culmina en la prueba de la identidad pitagórica y otras identidades trigonométricas.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
Module 2 builds on students' previous work with units and with functions from Algebra I, and with trigonometric ratios and circles from high school Geometry. The heart of the module is the study of precise definitions of sine and cosine (as well as tangent and the co-functions) using transformational geometry from high school Geometry. This precision leads to a discussion of a mathematically natural unit of rotational measure, a radian, and students begin to build fluency with the values of the trigonometric functions in terms of radians. Students graph sinusoidal and other trigonometric functions, and use the graphs to help in modeling and discovering properties of trigonometric functions. The study of the properties culminates in the proof of the Pythagorean identity and other trigonometric identities.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Algebra
Mathematics
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
Date Added:
08/15/2014