For the depth of water on Friday, 16 January 1998, the periodic function is:

Question

y = 1.05 sin 2pix/11.72 + 1.55

1.05 is the 'a' value
2pi/11.72 is the 'b' value
1.55 is the 'd' value
we were told not to take into consideration the 'c' value in our equation
'y' is equal to the depth of water
'x' is equal to the number of hours after 6am on Friday, 16 January (6am = 0x, 7am = 1x, 8am = 2x etc.)

the maximum height of water on the graph is 2.6m and the minimum height of the water is 0.5m

With using the equation, the question is asking during what time periods will the water be above 1.7m on Monday, 19 January (3 days later)

I have done this question two ways. I have worked out each individual equation from where x = 66 (12am on 19 January) until when x = 89 (11pm on 19 January)
I have also worked it out by making y = 1.7 and working out the two 'x' values that way. Doing it this way, I ended up with 6:16am and 11:36am.

Which way would be the more right way to do this question?

Answer 1

Took me a while, but I was sure that Steve had answered this for you
http://www.jiskha.com/display.cgi?id=1432887186
and again here
http://www.jiskha.com/display.cgi?id=1432801604

Answer 2

As you figured, 19 January starts 66 hours from x=0. So, you want values of x between 66 and 90 (midnight on Jan 19)

You can see that there are two periods during that time when y >= 1.7

http://www.wolframalpha.com/input/?i=plot+y+%3D1.05+sin%282pi%2F11.72+x%29+%2B+1.55%2C+y%3D1.7+for+66%3C%3Dx%3C%3D90

The actual endpoints of the intervals can be read off here:

http://www.wolframalpha.com/input/?i=solve+1.05+sin%282pi%2F11.72+x%29+%2B+1.55-1.7%3D0+for+66%3C%3Dx%3C%3D90