# Math Help - Trig

1. ## Trig

The depth of water at the entrance to a harbour t hours after low tide is D metres and can be modelled by the equation D= a+ b cos[c(t+d)] for the constants a,b,c and d

at t = 0, it is low tide and the depth is 2 metres.
At the next high tide, 6 hours later, the depth is 8 metres.

Find Exact values of a,b,c and given that all constants are positive..

any help with this i dont even have a start :S
thanks

2. Originally Posted by Tarik678
The depth of water at the entrance to a harbour t hours after low tide is D metres and can be modelled by the equation D= a+ b cos[c(t+d)] for the constants a,b,c and d

at t = 0, it is low tide and the depth is 2 metres.
At the next high tide, 6 hours later, the depth is 8 metres.

Find Exact values of a,b,c and given that all constants are positive..

any help with this i dont even have a start :S
thanks
The formula has 4 coefficients you need to find, a, b, c, d. To do that you need 4 "conditions" or 4 equations. You are given:
1. When t= 0, the depth is 2: 2= a+ bcos(d)
2. 6 hours later, when t= 6, the depth is 8: 8= a+ bcos(6c+ d).
3. When t= 0, the depth is minimum. The minimum of cos(x) is -1 and occurs when $x= -\pi/2$: 2= a- b and $d= -\pi/2$.
4. When5 t= 6, the depth is maximum. The maximum of cos(x) is 1 and occurs when $x= \pi/2$: 8= a+ b and $6c+ d= \pi/2$.