At a seaport, the depth of the water $h$ metres at a time $t$ hours during a certain day is given by this formula; $$h=1.8\sin[2\pi{t-4.00\over12.4}]+3.1$$ What is the maximum depth of the water? When does it occur?
I know the maximum depth is 4.9 metres but what I don't know is how to solve the second part of the question. Am I supposed to set $h=4.9$?
Given $h=1.8sin[2\pi{t-4.00\over12.4}]+3.1$
We have to find $\max{h}=\max{1.8sin[2\pi{t-4.00\over12.4}]+3.1}=1.8\max{\sin[2\pi{t-4.00\over12.4}]}+3.1$
And we know $\max{\sin[2\pi{t-4.00\over12.4}]}=1$, hence $\max{h}=1.8+3.1=4.9$
Now, to find time $t$ at which the maximum height occurs, solve for $t$ in $1=sin[2\pi{t-4.00\over12.4}]$, and one of the solutions will be ${\pi\over2}=2\pi{t-4.00\over12.4}\implies t=7.1$