a) The amplitude of the <em>sinusoidal</em> wave is 15.
b) The period of the <em>sinusoidal</em> wave is 0.5236.
c) The <em>phase</em> shift of the <em>sinusoidal</em> wave is - 1.338π.
d) The <em>vertical</em> shift of the <em>sinusoidal</em> wave is - 5.
e) The equation of the <em>sinusoidal</em> wave is y = 15 · sin [(12 · x - 1.338π)] - 5.
<h3>What is the equation of the sinusoidal graph?</h3>
Herein we have the graph of a <em>sinusoidal</em> wave, whose constants can be found by using the following expressions:
Amplitude - Vertical distance between the maximum and minimum of the function:
a = [10 - (- 20)] / 2
a = 15
The amplitude of the <em>sinusoidal</em> wave is 15.
Period - Horizontal distance between two <em>consecutive</em> maxima or two <em>consecutive</em> minima.
T = 2 · (0.3809 - 0.1191)
T = 0.5236
The period of the <em>sinusoidal</em> wave is 0.5236.
And the <em>angular</em> frequency is calculated by the following expression:
b = 2π /T
b = 2π / 0.5236
b = 12
The <em>angular</em> frequency of the <em>sinusoidal</em> wave is 12.
Vertical shift - The average of the minimum and maximum of the function.
k = (10 - 20) / 2
k = - 5
The <em>vertical</em> shift of the <em>sinusoidal</em> wave is - 5.
Phase shift - <em>Horizontal</em> translation of the <em>sinusoidal</em> wave, which can be found by algebraic handling:
0.3809 = 15 · sin [(12 · 0.3809) + c] - 5
5.3809 = 15 · sin [(12 · 0.3809) + c]
0.359 = sin [(12 · 0.3809) + c]
0.117π = (12 · 0.3809) + c
0.117π = 4.5708 + c
c = - 1.338π
The <em>phase</em> shift of the <em>sinusoidal</em> wave is - 1.338π.
The equation of the <em>sinusoidal</em> wave is y = 15 · sin [(12 · x - 1.338π)] - 5.
To learn more on sinusoidal waves: brainly.com/question/13260086
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