Respuesta :

The given signal is
(x) = -3 cos(4x + π) + 6

The amplitude is |-3| = 3
If T is the period, then
(2π)/T = 4
4T = 2π
T = π/2
The period is π/2.
The phase shift is -π/4.
The vertical shift is 6.

A graph of the function is shown below.

Answer:
Amplitude = 3.
Period = π/2.
Phase shift = -π/4

Ver imagen Аноним

The amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.

Periodic function

A periodic function is a function that repeats itself after a definite time interval.

Given

[tex]f(x) = -3cos(4x+\pi ) +6[/tex]

The cosine function is a periodic function that repeats itself in the interval of [tex]2\pi [/tex].

Step by step explanation

For maximun amplitude

[tex]cos(4x+\pi )=-1\\ [/tex]

Then

[tex]f(x)=3+6\\ f(x)= 9[/tex]

For time period

The cosine function repeats itself in the interval of [tex]2\pi [/tex].

[tex]\begin{aligned} \frac{2\pi }{T} &= 4 \\\\ T &=\dfrac{\pi }{2}\\ \end{aligned}[/tex]

For phase shift

Phase is   [tex]\dfrac{\pi }{4} [/tex]

Thus, the amplitude, period, and phase shift are 9, [tex]\dfrac{\pi }{2} [/tex] and [tex]\dfrac{\pi }{4} [/tex] respectively.

To more about the Period function link is given below.

https://brainly.com/question/8636691

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