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MATH 143 - Module 8 Discussion Questions If you are stuck on a particular problem before submitting the initial part, leave it blank or take your best gut feeling guess. Remember, you are graded on a complete initial post and a complete final repost of all problems. Show all steps. Including sketches is always helpful. 1. Solve for all solutions to 2cos 2t = V3 2. Solve for all solutions to sin 3xcos 2x + cos 3x sin 2x = 1 on [0, 2n) 3. Solve for all solutions 2 sint = 4 sin t + 6 on [0, 2n) 4. Simple Harmonic Motion: An object is attached to a coiled spring. It is pulled down a distance of 6 inches from its equilibrium position and released. The period of the motion is 4 seconds. a. Show your work for modeling an equation of the objects simple harmonic motion d = acos wt where d is distance from the rest position and the period is w, w > 0. A hand sketch may be helpful, but is not required. b. What is the frequency? c. When t = 3 find the distance and interpret it. 5. Show your work for modeling and solving: A surveyor needs to determine the distance between him and each of two points that lie on the opposite side of a canal. The straight-line distance between the two points on the opposite side of the canal is 450 yards. The angles from each end of the line segment to the point where the surveyor is standing on the near side of the canal are 570 and 69 respectively. Find the distance from the surveyor to each point on the opposite side of the canal. Round to the nearest hundredth yard