Question

Find the following of the given sinusoidal wave

Answer 1

a) The amplitude of the sinusoidal wave is 15.

b) The period of the sinusoidal wave is 0.5236.

c) The phase shift of the sinusoidal wave is - 1.338π.

d) The vertical shift of the sinusoidal wave is - 5.

e) The equation of the sinusoidal wave is y = 15 · sin [(12 · x - 1.338π)] - 5.

What is the equation of the sinusoidal graph?

Herein we have the graph of a sinusoidal 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 sinusoidal wave is 15.

Period - Horizontal distance between two consecutive maxima or two consecutive minima.

T = 2 · (0.3809 - 0.1191)

T = 0.5236

The period of the sinusoidal wave is 0.5236.

And the angular frequency is calculated by the following expression:

b = 2π /T

b = 2π / 0.5236

b = 12

The angular frequency of the sinusoidal wave is 12.

Vertical shift - The average of the minimum and maximum of the function.

k = (10 - 20) / 2

k = - 5

The vertical shift of the sinusoidal wave is - 5.

Phase shift - Horizontal translation of the sinusoidal 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 phase shift of the sinusoidal wave is - 1.338π.

The equation of the sinusoidal wave is y = 15 · sin [(12 · x - 1.338π)] - 5.

To learn more on sinusoidal waves: brainly.com/question/13260086

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