Answer
$y = 20 + 15 sin(\frac{πt}{6} + \frac{π}{3})$
Work Step by Step
Let $y = A+B sin(at +b)$. Since the maximum and minimum values of $y$ are $35$ and $5$, $A+B = 35$ and $A−B = 5$, $A = 20$, $B = 15$.
The period is 12 hours, so $12a = 2π$ and $a = \frac{π}{6}$.
The maximum occurs at $t = 1$, so $1 = sin(a + b) = sin(\frac{π}{6} + b)$,
$\frac{π}{6} + b = \frac{π}{2}$,
$b = \frac{π}{2} − \frac{π}{6} = \frac{π}{3}$ and
$y = 20 + 15 sin(\frac{πt}{6} + \frac{π}{3})$.
