The standard sine function is given by:
[tex]y=a\sin (bx+c)[/tex]
Where:
Amplitude = 2a
Period = 2π/b
Horizontal shift = c
In this case, we have:
- Maximum of 6 and minimum of negative 6, hence the amplitude is 12, this is
[tex]\begin{gathered} 2a=12 \\ \frac{2a}{2}=\frac{12}{2} \\ a=6 \end{gathered}[/tex]
- The period is 2π/3, therefore:
[tex]\begin{gathered} \frac{2\pi}{3}=\frac{2\pi}{b} \\ b\cdot2\pi=3\cdot2\pi \\ b\cdot\frac{2\pi}{2\pi}=3\cdot\frac{2\pi}{2\pi} \\ b=3 \end{gathered}[/tex]
- The graph passes through the y-axis at (0,2), which is 1/3 of the maximum. Considering the shift, we have
[tex]c=\pi[/tex]
Answer:
a = 6, b = 3, c = π
