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.

Students explore the concept of similar right triangles and how they apply to trigonometric ratios. Use this lesson as a refresher of what trig ratios are and how they work. In addition to trigonometry, students explore a clinometer app on an Android® or iOS® device and how it can be used to test the mathematics underpinning trigonometry. This prepares student for the associated activity, during which groups each put a clinometer through its paces to better understand trigonometry.

The Tippy Tap hand-washing station is an inexpensive and effective device used extensively in the developing world. One shortcoming of the homemade device is that it must be manually refilled with water and therefore is of limited use in high-traffic areas. In this activity, student teams design, prototype and test piping systems to transport water from a storage tank to an existing Tippy Tap hand-washing station, thereby creating a more efficient hand-washing station. Through this example service-learning engineering project, students learn basic fluid dynamic principles that are needed for creating efficient piping systems.

These Trigonometry lecture videos coterminal angles, trig functions, quadrantal angles, special acute angles, co-functions, finding theta, reference angles, trig functions, radian measure, arc length, area of a sector, graphing sine and cosine using t-table, amplitude and frequency, phase shift for sine and consine, vertical shift, tangent curve, cotangent transformations, evaluating trig identities, trig expressions, sum and difference for cosine, double and half angle identities, inverse, principal values, solving difficult trig equations, law of cosines, area of a triangle, and vectors and bearing.

Students investigate the relationships between angles and side lengths in right triangles with the help of materials found in the classroom and a mobile device. Using all or part of a meter stick or dowel and text books or other supplies, students build right triangles and measure the angles using a clinometer application on an Android® (phone or tablet) or iOS® device (iPhone® or iPad®). Then they are challenged to create a triangle with a given side length and one angle. The electronic device is used to measure the accuracy of their constructions.

(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.