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Pre-Calculus Practice Problem 191

# Pre-Calculus Practice Problem 191 - b If a boat can only...

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Unit 6, Activity 3, Solving Trigonometric Equations with Answers Blackline Masters, Advanced Math - Pre-Calculus Page Louisiana Comprehensive Curriculum, Revised 2008 189 7. Suppose that the height of the tide, h meters, at the harbor entrance is modeled by the function h = 2.5sin 30t o + 5 where t is the number of hours after midnight. a) When is the height of the tide 6 meters? If h = 6, 6 = 2.5sin 30t + 5 sin 30t = 0.4 30t = 23.58 or 156.42 t = 0.786 hours or 5.214 hours The height is 6 meters at 12:47 a.m. and 7:13 a.m. Since the period is 12 (12 hours) there is also 12 + 0.786 and 12 + 5.214 in the 24 hour period. This gives 12:47 p.m. and 5:13 p.m. The graph is shown below. The line represents the 6 meter tide.
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Unformatted text preview: b) If a boat can only enter and leave the harbor when the depth of the water exceeds 6 meters, for how long each day is this possible? Twice a day for 4 hours and 26 minutes. 8. How can you determine, prior to solving a trigonometric equation, how many possible answers you should have? Determine how many periods are in the interval in which the solutions lie and how many solutions are found within one period. This will give the total number of solutions. 5. cos 2 x + 2cos x + 1 = 0 (cos x + 1)(2cos x + 1) = 0 cos x = -1 x = 180 o 6 . 2sin 2 x = sin x 2sin 2 x – sin x= 0 sin x(2sin x – 1) = 0 sin x = 0 or sin x = ½ x = 0, 180 o , 30 o , 150 o...
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