Trigonometric functions define the angles in a triangle in terms of the relationship of two sides in that triangle. These tutorials cover the angle functions, with step-by-step instructions for working them out (and the opportunity to use your own numbers).

Atmosphere Applet: This program lets you study how the properties of the atmosphere change with altitude. You can study the atmosphere of either the Earth or Mars. The equations used in this program are taken from the ICAO standard day model for the Earth and from some curve fits of the Martian atmosphere gathered by the Global Surveyor spacecraft. Using the airplane graphic you can select an altitude, or you can type an altitude into the input box.

The program instantly outputs a selected property and displays the local temperature and pressure on gauges You can output the temperature, pressure, density, local speed of sound, Mach number for specified velocity, or the ratio of aircraft lift to the lift on Earth at sea level. Input and output can be given in either English or metric units.

This task was developed by high school and postsecondary mathematics and design/pre-construction educators, and validated by content experts in the Common Core State Standards in mathematics and the National Career Clusters Knowledge & Skills Statements. It was developed with the purpose of demonstrating how the Common Core and CTE Knowledge & Skills Statements can be integrated into classroom learning – and to provide classroom teachers with a truly authentic task for either mathematics or CTE courses.

The textbook "Calculus" by Gilbert Strang, is a modern calculus text written in a human-friendly style. Published in 1991 and still in print from Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.

This digital textbook was reviewed for its alignment with California content standards.

This 8-minute video lessons gives an example of using trig substitution to solve an indefinite integral. [Calculus playlist: Lesson 70 of 156]

This 8-minute video lesson looks at another example of finding an anti-derivative using trigonometric substitution. [Calculus playlist: Lesson 71 of 156]

This 18-minute video lesson shows an example using trig substitution (and trig identities) to solve an integral. [Calculus playlist: Lesson 72 of 156]

This 10-minute video lesson considers why the quotient rule is the same thing as the product rule. As well as an introduction to the derivative of e^x, ln x, sin x, cos x, and tan x. [Calculus playlist: Lesson 22 of 156]

Tnis 12-minute video lecture looks at an implicit differentiation example that involves the tangent function [Calculus playlist: Lesson 34of 156]

The University of California, Irvine Extension, supported by generous grants from the William and Flora Hewlett Foundation and The Boeing Company, is developing online courses to prepare science and mathematics teachers for the California Subject Examinations for Teachers (CSET).

UC Irvine Extension's online test-preparation courses correspond with the 10 CSET science subtests and three CSET mathematics subtests.

Accuracy of measurement in navigation depends very much on the situation. If a sailor's target is an island 200 km wide, sailing off center by 10 or 20 km is not a major problem. But, if the island were only 1 km wide, it would be missed if off just the smallest bit. Many of the measurements made while navigating involve angles, and a small error in the angle can translate to a much larger error in position when traveling long distances.

Accuracy of measurement in navigation depends very much on the situation. If a sailor's target is an island 200 km wide, sailing off center by 10 or 20 km is not a major problem. But, if the island were only 1 km wide, it would be missed if off just the smallest bit. Many of the measurements made while navigating involve angles, and a small error in the angle can translate to a much larger error in position when traveling long distances.

Students find and calculate the angle that light is transmitted through a holographic diffraction grating using trigonometry. After finding this angle, student teams design and build their own spectrographs, researching and designing a ground- or space-based mission using their creation. At project end, teams present their findings to the class, as if they were making an engineering conference presentation. Student must have completed the associated Building a Fancy Spectrograph activity before attempting this activity. This activity is best completed over four 60-minutes sessions.

This exercise has students determine how fast a dinosaur was moving based on the tracks it made. It allows students with minimal quantitative background to become motivated and begin to develop an appreciation for dimensional analysis as they see whether or not they could outrun the track-making dinosaurs. Measurements from any dinosaur track site can be used in this activity. Learning goals, context for use, teaching tips, materials, assessment tips and related resources are provided.

EngineSim was developed at the NASA Glenn Research Center in an effort to foster hands-on, inquiry-based learning in science and math. EngineSim is a simulator that models the design and testing of jet engines. The program works in two modes: Design Mode or Tunnel Test Mode. In the Design Mode, you can change design variables including the flight conditions, the engine size, the inlet performance, the turbo machinery compressor and turbine performance, the combustors or burner performance, or the nozzle performance. For a turbofan engine design you can also vary the fan performance and the bypass ratio. When you have a design that you like, you can switch to the Tunnel Test Mode, where you can vary only the flight conditions (airspeed, altitude, and throttle setting).

RangeGames uses jet engines to present a variety of math and physics problems. RangeGames includes a "Play Mode," in which nothing is recorded; a "Learn Mode," in which you will get several tries at determining the correct answer; and an "Exam Mode," where you get one chance and your answer is recorded for your teacher.

Rate and force problems of different levels of difficulty are included. These are targeted for the high school student. The rate problems deal with how far and how long an airplane can fly on a given amount of fuel. The force problems deal with Newton's laws of motion on takeoff. Graphical feedback is given for each answer choice.

This is a comprehensive math textbook for Grade 10. It can be downloaded, read on-line on a mobile phone, computer or iPad. Every chapter has links to on-line video lessons and explanations. Summary presentations at the end of each chapter offer an overview of the content covered, with key points highlighted for easy revision. Topics covered are: algebraic expressions, equations and inequalities, exponents, number patterns, functions, finance and growth, trigonometry, analytical geometry, statistics, probability, Euclidean geometry, measurements. This book is based upon the original Free High School Science Text series.

This is a comprehensive math textbook for Grade 11. It can be downloaded, read on-line on a mobile phone, computer or iPad. Every chapter has links to on-line video lessons and explanations. Summary presentations at the end of each chapter offer an overview of the content covered, with key points highlighted for easy revision. Topics covered are: language of mathematics, exponents, surds, error margins, quadratic sequences, finance, quadratic equations, quadratic inequalities, simultaneous equations, mathematical models, quadratic functions and graphs, hyperbolic functions and graphs, exponential functions and graphs, gradient at point, linear programming, geometry, trigonometry, statistics, independent variables, dependent events. This book is based upon the original Free High School Science Text series.

This is a comprehensive math textbook for Grade 12. It can be downloaded, read on-line on a mobile phone, computer or iPad. Every chapter has links to on-line video lessons and explanations. Summary presentations at the end of each chapter offer an overview of the content covered, with key points highlighted for easy revision. Topics covered are: language of mathematics, logarithms, sequences and series, finance, factorising cubic polynomials, functions and graphs, differential calculus, linear programming, geometry, trigonometry, statistics, combinations and permutations. This book is based upon the original Free High School Science Text series.

FoilSim II computes the theoretical lift of a variety of airfoil shapes. The user can control the shape, size, and inclination of the airfoil and the atmospheric conditions in which the airfoil is flying. The program includes a stall model for the airfoil, a model of the Martian atmosphere, and the ability to specify a variety of fluids for lift comparisons. The program has graphical and numerical output, including an interactive probe which you can use to investigate the details of flow around an airfoil.
Using the CurveBall applet, students learn more about aerodynamics by controlling conditions of a big league baseball pitch, including altitude(location), speed of pitch, and spin of pitch. The latest version has the ability to specify atmospheric conditions for the baseball game.