From looking at a periodic function, we had to decide on the equation for it. I got:

Question

y = 1.05 sin x2pi/11.72 + 1.55

1.05 is the 'a' value of the equation
2pi/11.72 is the 'b' value for the equation
1.55 is the 'd' value of the equation
we were told not to take into consideration the 'c' value at all.

the minimum of the graph is 0.5, the maximum is 2.6 and 11.72 is the period

the function showed the depth of water on the 16 January and displayed the times of 6am to 11pm (where 6am = 0x, 7am = 1x ....... 11pm = 17x)

The question is asking what time periods will the water be 1.7 and over on the 19 January.

Answer 1

ok. you have

y = 1.05 sin(2π/11.72 x) + 1.55

So, when does y=1.7?

1.05 sin(2π/11.72 x) + 1.55 = 1.7
1.05 sin(0.5361x) = 0.15
sin(0.5361x) = 0.1428
.5361x = 0.1433 or 2.9982
That means that x = 0.2673 or 5.5926
So, y >= 1.7 when 0.2673 <= x <= 5.5926
Or, between 6:16 and 11:35

Answer 2

I understand how you got 0.1433 and 2.9982 from using the CAST diagram, I'm just wondering why you need to do that?
And I'm not sure how you converted 0.2673 and 5.5926 into hours and minutes

Answer 3

Don't really need to do it. I was just showing the logical steps I followed.

As for the conversion to hours and minutes, well, duh: 60 minutes in an hour, so .2673 hours is .2673*60 or about 16 minutes.

Answer 4

does that mean it'll be above 1.7m from 6:16pm to 11:35pm as well?