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# Trigonometry

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In one day, there are two high tides and two low tides in equally spaced intervals. The high tide is observed to be 6 feet above the average sea level. After 6 hours pass, the low tide occurs at 6 feet below the average sea level. In this task, you will model this occurrence using a trigonometric function by using x as a measurement of time. Assume the first high tide occurs at x = 0.

Part B
Determine these key features of the function that models the tide:

amplitude
period
frequency
midline
vertical shift
phase shift

Part C
Create a trigonometric function that models the ocean tide for a period of 12 hours.

Part E
What is the height of the tide after 93 hours?

Jul 23, 2019

#1
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Amplitude  =  (highest - lowest)/2 = 6 - -6  /2  = 12/2 = 6 feet

period = time for 1 cycle   from high to low to high = 6 + 6 = 12 hours

frequency = 1/period   = 1/12   cycles per hour

midline = 0  (midpoint between high and low)

Vertical shift = 0    the high and the low are equal in magnitude

Phase shift = 0 if using cosine function to model this     or  90 degrees  (pi/2) leftward if using sine

Usual cos period is 2pi

we want 1/12 of the        1/12 x 2pi = pi/6

6 cos ( (pi/6) *x) = height    or     6 sin ((pi/6)( x) + pi/2))

6 cos (pi/6 x)    when x = 93    6 cos (93pi/6) = 0 ft

Here is the graph:

https://www.desmos.com/calculator/3pv8ltv8xh

Jul 23, 2019

#1
0

Amplitude  =  (highest - lowest)/2 = 6 - -6  /2  = 12/2 = 6 feet

period = time for 1 cycle   from high to low to high = 6 + 6 = 12 hours

frequency = 1/period   = 1/12   cycles per hour

midline = 0  (midpoint between high and low)

Vertical shift = 0    the high and the low are equal in magnitude

Phase shift = 0 if using cosine function to model this     or  90 degrees  (pi/2) leftward if using sine

Usual cos period is 2pi

we want 1/12 of the        1/12 x 2pi = pi/6

6 cos ( (pi/6) *x) = height    or     6 sin ((pi/6)( x) + pi/2))

6 cos (pi/6 x)    when x = 93    6 cos (93pi/6) = 0 ft

Here is the graph:

https://www.desmos.com/calculator/3pv8ltv8xh

ElectricPavlov Jul 23, 2019