Содержание
- 2. Lecture Outline The Law of Sines The Law of Cosines Harmonic motion
- 3. Introduction Triangles are everywhere, and we often need to find unknown angles or the side lengths.
- 4. The Law of Sines The Law of Sines says that in any triangle the lengths of
- 5. Proof: The Law of Sines
- 6. Example 1. A satellite orbiting the earth passes directly overhead at observation stations in Phoenix and
- 7. Solution The distance of the satellite from L.A. is about 416 miles.
- 8. Your turn! Solve the triangle in the following figure. Here, “solve” means find all unknown angles
- 10. Example 2
- 11. The Law of Cosines
- 12. Proof: The Law of Cosines
- 13. Example 3. A tunnel is to be built through a mountain. To estimate the length of
- 15. Your turn!
- 16. Solution
- 17. You need to consider given information and decide whether to use the law of sines or
- 18. Solution
- 19. Your turn!
- 20. Solution
- 21. Harmonic motion Periodic behavior – behavior that repeats over and over again – is common in
- 22. Simple harmonic motion
- 23. Find the amplitude, period, and frequency of the motion of the mass. (b) Sketch a graph
- 24. Solution (b)
- 25. Your turn!
- 26. Solution (b)
- 27. The tone of the sound depends on the frequency, and the loudness depends on the amplitude.
- 29. Solution The amplitude will increase, so the number 0.2 is replaced by a larger number.
- 31. Example 6 The number of hours of daylight varies throughout the course of a year. In
- 33. Solution
- 34. Solution(continued)
- 35. Solution(continued) That is, from Jan 1 to Apr 10 and from Aug 30 to Dec 31,
- 37. Solution
- 38. Damped harmonic motion The amplitude of a spring in a frictionless environment will not change. The
- 40. Simple harmonic vs. damped harmonic motion
- 41. Example 7
- 42. Solution
- 43. Solution(continued)
- 44. Example 8
- 45. Solution
- 46. Learning outcomes 3.5.1. Solve triangles by using the law of sines and the law of cosines
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