The water level in a coastal inlet has a maximum depth of 4 meters above the mean level at 8 am, and has a period of 12.4 hrs. The trigonometric equation for modelling the tidal depth has to be found.
The given equations are all cosine graphs. The general formula for a cosine graph is:
[where A=amplitude of the function = (max.-min.)/2 (vertical stretch of the graph), B=stretch/shrink on the x-axis, it is related to period as: `B=(2pi)/P` , C/B is the phase shift of the graph, and V=vertical shift of the graph]
Here, maximum depth of water is 4 meters above the mean level. So, minimum depth should be 4 meters below mean level.
Here only option C) has A=4, hence it is the correct answer.
Other constants, i.e. B, C and D can also be checked from the given relationships.