Answer:
[tex]y=3\text{Sin}[\frac{1}{2}(x-\frac{\pi}{4})] -1[/tex]
Step-by-step explanation:
Let the equation of the sine wave is,
y = Asin[B(x + C)] + D
Where A = Amplitude
B = [tex]\frac{2\pi}{\lambda}[/tex] (λ = wavelength)
C = Horizontal shift of the wave
D = Vertical shift of the wave
From the figure attached,
Since, wave has been shifted 1 unit down and [tex]\frac{\pi}{4}[/tex] units right.
C = -[tex]\frac{\pi }{4}[/tex]
D = -1
λ = [tex]\frac{17\pi}{4}-\frac{\pi}{4}[/tex]
= [tex]\frac{16\pi}{4}[/tex]
= 4π
B = [tex]\frac{2\pi }{4\pi }[/tex] = [tex]\frac{1}{2}[/tex]
Amplitude 'A' = [tex][\frac{2-(-4)}{2}][/tex] = 3
Therefore, equation for the sine wave will be,
[tex]y=3\text{Sin}[\frac{1}{2}(x-\frac{\pi}{4})] -1[/tex]
