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Argument 209 Unit 1 Assignment

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Task #4: SUBDOMAIN 209.3 - PRECALCULUS
Competency 209.3.3: Trigonometric Equations and Identities
Jennifer Moore
Western Governor’s University

Part 1:
Based on Section 5.5 Graphs of Sine and Cosine Functions (Blitzer, 2013), the function can be used to exhibit the periodic behavior of water depth. A is amplitude, B can be used to find the period, B and C together are used to find the phase shift, and D is the vertical shift. The amplitude is defined as the difference between the maximum and minimum value divided by two, . The period is defined as . The phase shift is defined as , and the vertical shift, D, is found by taking the mean, or average, of the maximum and minimum values, (Thinkwell, 2001). The information above is what is used to find the water depth, y, during an amount of time, t (in hours) after midnight using the format, replacing t with x for this problem. …show more content…
Given: y = A cos(Bx − C) + D. Throughout the day the depth of water at the end of a pier varies with the tides. High tide occurs at 4:00 a.m. with a depth of 6 meters. Low tide occurs at 10:00 a.m. with a depth of 2 meters.
To find , A, B, C, and D have to be solved. Below is the solution in terms of t, hours after midnight: The vertical shift, D, is found by using the maximum, high tide, and minimum, low tide, and finding the mean, average. The amplitude is the difference between high tide and low tide. Once that is done, divide the solution by

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