Watch the development of the sine curve and the cosine curve by tracing the unit circle in this fascinating applet.

The tutorial investigates period and frequency by examining the shapes of the sine and cosine functions. The resource consists of definitions, animations, interactive graphs, and examples. Practice problems with solutions are included.

Students come to see the exponential trend demonstrated through the changing temperatures measured while heating and cooling a beaker of water. This task is accomplished by first appealing to students' real-life heating and cooling experiences, and by showing an example exponential curve. After reviewing the basic principles of heat transfer, students make predictions about the heating and cooling curves of a beaker of tepid water in different environments. During a simple teacher demonstration/experiment, students gather temperature data while a beaker of tepid water cools in an ice water bath, and while it heats up in a hot water bath. They plot the data to create heating and cooling curves, which are recognized as having exponential trends, verifying Newton's result that the change in a sample's temperature is proportional to the difference between the sample's temperature and the temperature of the environment around it. Students apply and explore how their new knowledge may be applied to real-world engineering applications.

Principles of Macroeconomics 2e covers the scope and sequence of most introductory economics courses. The text includes many current examples, which are handled in a politically equitable way. The outcome is a balanced approach to the theory and application of economics concepts. The second edition has been thoroughly revised to increase clarity, update data and current event impacts, and incorporate the feedback from many reviewers and adopters. Changes made in Principles of Macroeconomics 2e are described in the preface and the transition guide to help instructors transition to the second edition. The first edition of Principles of Macroeconomics by OpenStax is available in web view here.

By the end of this section, you will be able to:

Contrast expansionary monetary policy and contractionary monetary policy
Explain how monetary policy impacts interest rates and aggregate demand
Evaluate Federal Reserve decisions over the last forty years
Explain the significance of quantitative easing (QE)

Watch as water pushes against soft soil, shifting rivers into the meandering water flows that we can observe on maps from high above around the Earth. [2:56]

Learn how a car traveling at a constant speed around a curve is actually accelerating. This video explains how acceleration not only involves a change in speed but also a change in direction. [4:49]

Khan Academy learning modules include a Community space where users can ask questions and seek help from community members. Educators should consult with their Technology administrators to determine the use of Khan Academy learning modules in their classroom. Please review materials from external sites before sharing with students.

This site is an example of the use of exponential decay. The example involves the effectiveness of a medical dosage over time.