How do I solve this trigonometry biorhythms problem?

Question

Let $y = \sin(at + b)$ (in degrees) and let $t$ be the number of days.

1. If there are $30$ days between the peaks of this function (positive peaks), show that $a = 12$.
2. If the last peak (positive) occurred exactly $7000$ days from the start, explain why $b = -30$.

Answer 1

1. You might want to explain "there are $30$ days between the peaks of this functions" in mathematical terms. Hint: there is a mathematical relation between $a$ and the distance between two consecutive peaks (if $a=1$ by example, the distance between two consecutive peaks would be $360$ days, since one needs to go all over these $360$ degrees to get from on peak to the next).
2. At $7000$ days from the start, the value of the function is $\sin(a\times 7000+b)$. Since it is a peak, the value is equal to $1$. Knowing $a$, one should be able to solve for $b$.