Answer:
[tex]y=2sin[\frac{\pi}{4}(x+3) ]-5[/tex]
Step-by-step explanation:
The standard form for a sinusoidal function is given by:
y = Asin[B(x - C)] + D
Where A is the amplitude of the sine wave, the period is 2π/B, C is the phase shift and D is the vertical displacement / translation
Given:
A = 2, D = -5 (down), C = -3 (left).
8 = 2π/B; B = π/4
Therefore:
[tex]y=2sin[\frac{\pi}{4}(x+3) ]-5[/tex]
