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.

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.

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.

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 

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).

Modeling Our World with Mathematics Unit 6: The Arts Topic 1 - Catch a Wave with Music

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.

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.

(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.