1. Write the equation of a sine function with the given amplitude and period. a) $\operatorname{amp}=2$, per $=1080^{\circ}$ b) amp $=\frac{3}{2}$, per $=6 \pi$

Step 1 ：The general form of a sine function is \(y = A\sin(B(x - C)) + D\) where \(A\) is the amplitude, \(B\) is the frequency, which is related to the period by the formula \(B = \frac{2\pi}{\text{period}}\), \(C\) is the phase shift, and \(D\) is the vertical shift.

Step 2 ：For part a), the amplitude is 2 and the period is 1080 degrees. We need to convert the period from degrees to radians because the sine function uses radians. The conversion factor is \(\frac{\pi}{180}\) radians per degree. So, the period in radians is \(6\pi\). The frequency \(B\) is then \(\frac{1}{3}\). So, the equation of the sine function is \(y = 2\sin\left(\frac{x}{3}\right)\).

Step 3 ：For part b), the amplitude is \(\frac{3}{2}\) and the period is \(6\pi\). The frequency \(B\) is \(\frac{1}{3}\). So, the equation of the sine function is \(y = \frac{3}{2}\sin\left(\frac{x}{3}\right)\).

Step 4 ：\(\boxed{\text{Final Answer: The equations of the sine functions are }}\)

Step 5 ：\(\boxed{a) y = 2\sin\left(\frac{x}{3}\right)}\)

Step 6 ：\(\boxed{b) y = \frac{3}{2}\sin\left(\frac{x}{3}\right)}\)