Answer:
y = 4 sin( 0.5t - [tex]\frac{4\pi }{3}[/tex] ) - 2
y = a sin ( 2t - [tex]\frac{-\pi }{3}[/tex]) + 2
Step-by-step explanation:
In the first question,
amplitude = 4
Period = [tex]4\pi[/tex]
phase shift = [tex]\frac{-4\pi }{3}[/tex]
Vertical shift = -2
Angular velocity , w = [tex]\frac{2\pi }{time period}[/tex]
Here, w = [tex]\frac{2\pi }{4\pi }[/tex] = 0.5
The general equation of a wave is
y = a sin( wt + ∅ )
Putting above values in the equation,
y = 4 sin( 0.5t - [tex]\frac{4\pi }{3}[/tex] ) - 2
In the second question,
Amplitude is not given so we will take it as a.
time period = [tex]\pi[/tex]
w = 2
Phase shift = [tex]\frac{-\pi }{3}[/tex]
Vertical shift = 2
The equation is
y = a sin ( 2t - [tex]\frac{-\pi }{3}[/tex]) + 2
