a \sin(c) = 0 \implies \sin(c) = 0 \implies c = 0 \quad \text{(since sine is zero at multiples of } \pi\text{, and we want minimal phase shift)}
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- The wave passes through the origin, so \( f(0) = 0 \):
- f(0) = a \sin(c) + d = 0
- Since the maximum amplitude is 3, the midline is likely centered at 0 (symmetric about \( y = 0 \)), so \( d = 0 \). Then:
- Thus, \( a = 3 \), \( b = 2 \), \( c = 0 \), \( d = 0 \).
- The function becomes \( f(x) = 3\sin(2x) \), which satisfies all conditions.
- Final values:
