In this lesson, students will learn that math is important in navigation and engineering. Ancient land and sea navigators started with the most basic of navigation equations (Speed x Time = Distance). Today, navigational satellites use equations that take into account the relative effects of space and time. However, even these high-tech wonders cannot be built without pure and simple math concepts basic geometry and trigonometry that have been used for thousands of years. In this lesson, these basic concepts are discussed and illustrated in the associated activities.

This task applies geometric concepts, namely properties of tangents to circles and of right triangles, in a modeling situation. The key geometric point in this task is to recognize that the line of sight from the mountain top towards the horizon is tangent to the earth. We can then use a right triangle where one leg is tangent to a circle and the other leg is the radius of the circle to investigate this situation.

This resource is a collection of full hour-long lectures and accompanying notes covering most of chapters 6-10 of the OpenStax Algebra and Trigonometry book. The notes are provided in both .DOCX and .PDF format to accommodate downloading ease. Students should be encouraged to print notes and fill them out as they watch through the lectures.

PowerPoint Slides to accompany Chapter 10 (Sections 10.1, 10.2 and 10.3) of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

PowerPoint Slides to accompany Chapter 10 (Section 10.5) of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

PowerPoint Slides to accompany Chapter 10 (Section 10.8) of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

PowerPoint Slides to accompany Chapter 7 of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

PowerPoint Slides to accompany Chapter 8 of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

PowerPoint Slides to accompany Chapter 9 of OpenStax Algebra and Trigonometry textbook. Prepared by River Parishes Community College (Jared Eusea, Assistant Professor of Mathematics, and Ginny Bradley, Instructor of Mathematics) for OpenStax Algebra and Trigonometry textbook under a Creative Commons Attribution-ShareAlike 4.0 International License. Date provided: July 2019.

This OER course using a new textbook is based a section of MAT103 Pre-Calculus. It is a preparatory course for Calculus. It builds upon the intermediate level of Algebra and makes intensive use of technology to conceptualize functions and methods of function manipulation with emphasis on quantitative change. All course content written by Fahmil Shah. Added to OER Commons by Victoria Vidal.

Word Count: 5097

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

A preparation for MAT 201 and the physical sciences. Students study principles, properties, and

applications of functions and their graphs. They revisit functions introduced in MAT 107 and expand

their knowledge of them. The course focuses heavily on circular trigonometric functions and introduces

conic sections. Laboratory activities place particular emphasis on the use of functions to model real

problems. Computers and/or graphing calculators are used to enhance the study of mathematics.

Prerequisites: A grade of C- or better in MAT 107 or a score of 71 or higher on the College Level Math

placement test; ENG 090 and ENG 094 (COL 090), or satisfactory placement test scores.

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus sequence including trigonometry. The first portion of the book is an investigation of functions, exploring the graphical behavior of, interpretation of, and solutions to problems involving linear, polynomial, rational, exponential, and logarithmic functions. An emphasis is placed on modeling and interpretation, as well as the important characteristics needed in calculus.

This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle.  New tools are introduced for solving geometric and modeling problems through the power of trigonometry.  Students explore sine, cosine, and tangent functions and their periodicity, derive formulas for triangles that are not right, and study the graphs of trigonometric functions and their inverses.

(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.)

Este módulo revisa la trigonometría que se introdujo en la geometría y el álgebra II, uniendo y ampliando aún más las ideas de la trigonometría del triángulo recto y el círculo unitario. Se introducen nuevas herramientas para resolver problemas geométricos y de modelado a través del poder de la trigonometría. Los estudiantes exploran funciones sinuso, coseno y tangentes y su periodicidad, derivan fórmulas para triángulos que no son correctos y estudian los gráficos de las funciones trigonométricas y sus inversos.

English Description:
This module revisits trigonometry that was introduced in Geometry and Algebra II, uniting and further expanding the ideas of right triangle trigonometry and the unit circle.  New tools are introduced for solving geometric and modeling problems through the power of trigonometry.  Students explore sine, cosine, and tangent functions and their periodicity, derive formulas for triangles that are not right, and study the graphs of trigonometric functions and their inverses.

This is the Project MathTalk homepage that has videos on the following topics: Parabolas, Proportions, Algebraic Expressions, Exponentials, Logarithms, Binomials, Trigonometry, and more.  Over 400 FREE, short, online videos that feature students working on mathematics problems and resolving their struggles through conversation. The instructional approach to the videos draws on evidence-based practices from the latest research in mathematics education. Engaging with the videos enables learners to explore conceptually rich mathematics problems by watching other students talk about math problems via an accessible online platform. The site also contains useful materials for teachers, researchers, and teacher educators. 

This resource contains information which may be used by students for self-directed learning. Teachers may use it to supplement their lessons.

Students analyze a cartoon of a Rube Goldberg machine and a Python programming language script to practice engineering analysis. In both cases, they study the examples to determine how the different systems operate and the function of each component. This exercise in juxtaposition enables students to see the parallels between a more traditional mechanical engineering design and computer programming. Students also gain practice in analyzing two very different systems to fully understand how they work, similar to how engineers analyze systems and determine how they function and how changes to the system might affect the system.

Working in small groups, students complete and run functioning Python codes. They begin by determining the missing commands in a sample piece of Python code that doubles all the elements of a given input and sums the resulting values. Then students modify more advanced Python code, which numerically computes the slope of a tangent line by finding the slopes of progressively closer secant lines; to this code they add explanatory comments to describe the function of each line of code. This requires students to understand the logic employed in the Python code. Finally, students make modifications to the code in order to find the slopes of tangents to a variety of functions.