graph the given function. state the period, amplitude, phase shift, and vertical shift of the function.\n$y…

graph the given function. state the period, amplitude, phase shift, and vertical shift of the function.\n$y = 4\\sin(x)$\nclear all draw:\nperiod:\namplitude:\nphase shift:\nvertical shift:\nquestion help: video ebook written example message instructor

graph the given function. state the period, amplitude, phase shift, and vertical shift of the function.\n$y = 4\\sin(x)$\nclear all draw:\nperiod:\namplitude:\nphase shift:\nvertical shift:\nquestion help: video ebook written example message instructor

Answer

Explanation:

Step1: Recall the general form of sine function

The general form of a sine function is (y = A\sin(B(x - C))+D), where (A) is the amplitude, (\frac{2\pi}{|B|}) is the period, (C) is the phase - shift, and (D) is the vertical shift.

Step2: Identify the values for the given function (y = 4\sin(x))

For the function (y = 4\sin(x)), we can rewrite it as (y=4\sin(1\times(x - 0))+0).

  • Amplitude: The formula for amplitude is (|A|). Here, (A = 4), so the amplitude (|A|=4).
  • Period: The formula for the period is (T=\frac{2\pi}{|B|}). Since (B = 1), then (T=\frac{2\pi}{|1|}=2\pi).
  • Phase - shift: The formula for phase - shift is (C). Here, (C = 0), so there is no phase shift.
  • Vertical - shift: The formula for vertical - shift is (D). Here, (D = 0), so there is no vertical shift.

Answer:

Period: (2\pi) Amplitude: (4) Phase Shift: (0) Vertical Shift: (0)