Describe the transformations and sketch the graphs of the following trigonometric functions f(x)=-2 \cos(2x)+3\ b. g(x)=3 \sin (x-\pi)-1

Burhan Hopper

Burhan Hopper

Answered question

2021-08-08

Describe the transformations and sketch the graphs of the following trigonometric functions. a.f(x)=2cos(2x)+3b.g(x)=3sin(xπ)1

Answer & Explanation

Brighton

Brighton

Skilled2021-08-09Added 103 answers

Step 1
We know y=Asin(BxC)+D is general equation of a sin function.
where |A| is amplitude, 2π|B| is time period, CB is Phase shift and D is vertical shift
(a)
f(x)=2cos(2x)+3
=2sin(π22x)+3
=2sin(2x+π2)+3
Amplitude =2
Time Period =2π2
=π
Phase shift =π22
=π4
Vertical shift =3
image

Step 2
(b)
g(x)=3sin(xπ)1
Amplitude =3
Time Period =2π1
=2π
Phase shift =π1
=π
Vertical shift =1
image Answer: Compare given equation with general equation of a sin function i.e. y=Asin(BxC)+D

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