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.

Precalculus 1 & 2 / Trigonometry provides a study of functions and their graphs, including polynomial, rational, exponential, and logarithmic functions. Additionally, right-triangle trigonometry, trigonometric functions and their applications are covered.

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.

Póngase Critical Equipo STEM. El Centro de Extensión y Educación en Ciencias Naturales colabora con la facultad de CSU, los Parques Nacionales y los programas de ciencia ciudadana para traducir su investigación científica actual en experiencias STEM únicas para los estudiantes en forma de kits educativos que se pueden prestar. Cada kit contiene casi todos los materiales necesarios (menos cosas comunes como agua y toallas de papel) para explorar algunos temas de investigación científica realmente interesantes. enviando un formulario de recogida local o un formulario de entrega disponible en el sitio web vinculado. Utilice la información de contacto en la página de descripción general del kit STEM para obtener más información. https://www.cns-eoc.colostate.edu/stem-kits/ Este kit se proporciona de forma gratuita para uso educativo.

RocketModeler was developed at the NASA Glenn Research Center in an effort to foster hands-on, inquiry-based learning in science and math. RocketModeler is a simulator that models the design and flight of a model rocket. The program works in two modes: Design Mode or Flight Mode. In the Design Mode, you can change design variables including the size of the rocket body, the fins, and the nose cone. You can also select different materials for each component. You can select from a variety of standard solid rocket engines. The program computes the center of gravity and pressure for your rocket and determines the stability. When you have a design that you like, you can switch to the Flight Mode (shown below), where you can launch your rocket and observe its flight trajectory. You can pause at any time to record data and then continue the flight through parachute deploy and recovery. This program has recently (Oct 8, 2004) been upgraded to support stomp rockets, bottle rockets, and ballistic shells in addition to solid model rockets. It also supports both English and metric units.

This modeling task involves several different types of geometric knowledge and problem-solving: finding areas of sectors of circles (G-C.5), using trigonometric ratios to solve right triangles (G-SRT.8), and decomposing a complicated figure involving multiple circular arcs into parts whose areas can be found (MP.7).

This task is intended to help model a concrete situation with geometry. Placing the seven pennies in a circular pattern is a concrete and fun experiment which leads to a genuine mathematical question: does the physical model with pennies give insight into what happens with seven circles in the plane?

This is a foundational geometry task designed to provide a route for students to develop some fundamental geometric properties that may seem rather obvious at first glance. In this case, the fundamental property in question is that the shortest path from a point to a line meets the line at a right angle, which is crucial for many further developments in the subject.

Students learn about and use a right triangle to determine the width of a "pretend" river. Working in teams, they estimate of the width of the river, measure it and compare their results with classmates.

CK-12 Foundation's Trigonometry FlexBook is an introduction to trigonometry for the high school student. It includes chapters on graphs of trigonometric functions, trigonometric identities, inverse trigonometric functions, triangles and vectors, and the polar system.

CK-12 Foundation's Trigonometry FlexBook is an introduction to trigonometry for the high school student. Topics include: Trigonometric Identities & Equations, Circular Functions, and Polar Equations & Complex Numbers.

CK-12's Texas Instruments Trigonometry Student Edition Flexbook is a helpful companion to a trigonometry course, providing students with more ways to understand basic trigonometric concepts through supplementary exercises and explanations.

CK-12's Texas Instruments Trigonometry Teacher's Edition Flexbook is a helpful companion to a trigonometry course, providing students with more ways to understand basic trigonometric concepts through supplementary exercises and explanations.

CK-12 Trigonometry Teacher's Edition provides tips and common errors for teaching CK-12 Trigonometry Student Edition. The solution and assessment guides are available upon request.

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.

Students learn about trigonometry, geometry and measurements while participating in a hands-on interaction with LEGO® MINDSTORMS® NXT technology. First they review fundamental geometrical and trigonometric concepts. Then, they estimate the height of various objects by using simple trigonometry. Students measure the height of the objects using the LEGO robot kit, giving them an opportunity to see how sensors and technology can be used to measure things on a larger scale. Students discover that they can use this method to estimate the height of buildings, trees or other tall objects. Finally, students synthesize their knowledge by applying it to solve similar problems. By activity end, students have a better grasp of trigonometry and its everyday applications.