Find the amplitude, period, and phase shift of y = 2 sin(r-)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Find the amplitude, period, and phase shift of y = 2 sin(r-)
Transcribed Image Text:Find the amplitude, period, and phase shift of y = 2 sin(r-)
Expert Solution
Step 1

The given function is 

y=2sin12x-π4               1

Consider the standard sin function with amplitude, period and phase shift

y=asinbx-c+d              2

Where, a is the amplitude of the function, 2πb is the period of the function and cb is the phase shift of the function

Now, compare (1) and (2) then

a=2,b=12,c=π4,d=0

So, the amplitude of the function is 2.

Period of the function

2πb=2π12=2π×2=4π

Hence, the required period of the function is 4π.

The phase shift of the function

cb=π412=π4×21=π2

Hence, the required phase shift of the function is π2

 

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