1993 - 9b (1 Viewer)

[bmn]

2U93-9b)!
Theres a pic here, but basically its a sin/cos graph, with amplitude of 1.73, but starts at (0, 1.35), goes to 1.73 then down like normal
Does a full revolution in 12.42h
Starts at 0:00h

The diagram shows the tidal effect due to the Moon at Port Hedland on 1 January 1900. The water level can be approximated by a sine curve of the form y = Asin(at + b) where y is the water level in metres measured as on the diagram and t is the time in hours after 0:00 hours.
i. Find the amplitude A.
ii. Estimate b by letting t = 0.
iii. Estimate a.
« i) 1.73m ii) b = 0.8952 (to 4 d.p.) iii) a = 0.5059 (to 4 d.p.) »

I've done i/ii easily, and I understand how to do iii, but I just can't seem to do it and get the right answer.

 

[boxhunter91]

I've done i/ii easily, and I understand how to do iii, but I just can't seem to do it and get the right answer.

Period = 2pi/n
now n=a
.: Period (12.42) = 2pi/a
.:a=2pi/12.42
.:a=0.51

 

[bmn]

Thanks, but why is n now a?

 

[boxhunter91]

Thanks, but why is n now a?

think of it like sin 2x
the 2 is the number of times a period is completed..
so in the equation a is the period.
Then you can see where im coming from.

 

[bmn]

think of it like sin 2x
the 2 is the number of times a period is completed..
so in the equation a is the period.
Then you can see where im coming from.

Ok, I get that, but what about the t and b?