8 A Look Back In Chapter 6, we defined the six trigonometric functions using the unit circle. In particular, we learned to evaluate the trigonometric functions. We also learned how to graph sinusoidal functions. In Chapter 7, we defined the inverse trigonometric functions and solved equations involving the trigonometric functions. A Look Ahead In this chapter, we define the trigonometric functions using right triangles and then use the trigonometric functions to solve applied problems. The first four sections deal with applications involving right triangles and oblique triangles , triangles that do not have a right angle. To solve problems involving oblique triangles, we will develop the Law of Sines and the Law of Cosines. We will also develop formulas for finding the area of a triangle. The final section deals with applications of sinusoidal functions involving simple harmonic motion and damped motion. Outline 8. 1 Right Triangle Trigonometry; Applications 8. 2 The Law of Sines 8. 3 The Law of Cosines 8. 4 Area of a Triangle 8. 5 Simple Harmonic Motion; Damped Motion; Combining Waves Chapter Review Chapter Test Cumulative Review Chapter Project Applications of Trigonometric Functions The Lewis and Clark Expedition In today’s world of GPS and smart phone apps that can precisely track one’s location, it is difficult to fathom the magnitude of the challenge that confronted Meriwether Lewis and William Clark in 1804. But Lewis and Clark managed. Commissioned by President Thomas Jefferson to explore the newly purchased Louisiana Territory, the co-captains led their expedition—the Corps of Discovery—on a journey that took nearly two and a half years and carried them more than 7000 miles. Starting at St. Louis, Missouri, they traveled up the Missouri River, across the Great Plains, over the Rocky Mountains, down the Columbia River to the Pacific Ocean, and then back. Along the way, using limited tools such as a compass and octant, they created more than 130 maps of the area with remarkable detail and accuracy. —See Chapter Project II— 545 Credit: Michael Warwick/Shutterstock
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