Question

The depth of water(d metres) in a harbour is given by the formula d = a+bsin(ct) where a, b and c are constants, and t is the time in hours after midnight. It is known that both b and c are non-zero and 20<c<35. If t=midnight, d=5; if t=noon, d=5; if t=1300, d=7; and if t=1400, d=8.46. Using the pieces of information, find the values of a,b and c

I already found the a, which turned out to be 5 and it's right. I found it by using the formula 5=a+bsin(c0) and since anytime sin is times by 0, you get 0, then a=5.

Answer 1

This is a 9th grade math problem by the way.

Answer 2

So, now you know that

d(t) = 5+b sin(ct)
Now plug in the values you know:

b sin(12c) = 0
b sin(1300c) = 2
b sin(1400c) = 3.46

we can see that 12c is a multiple of π.
So,
sin(1300c) = sin(1296c+4c) = sin(4c)
sin(1400c) = sin(1392c+8c) = sin(8c)

Hmmm. I'm stuck. 4c and 8c are both multiples of π/3, which have the same value for the sine. So, how can be be different?

Am I off base here?