1. Sep 1, 2010

### laura11

The tide in a local costal community can be modelled using a sine function. Starting at noon, the tide is at its "average" height of 3 metres measured on a pole located off of the shore. 5 hours later is high tide with the tide at a height of 5 metres measured at the same pole. 15 hours after noon is low tide with the tide at a height of 1 metre measured at the same pole. Use this information to model the tide motion using a sine function. Show all work.

2. Sep 1, 2010

### Office_Shredder

Staff Emeritus
What have you tried so far? Do you know what a general sinusoidal function is going to look like in equation form?

3. Sep 1, 2010

### laura11

i know the period is 12 hours which will be pi/6 in the equation
im pretty sure the amplitude is 2
so i know its going to be something like y=2sin(pi/6x)
but thn i dont know the vertical shift or horizontal shift

4. Sep 1, 2010

### laura11

the phase shift is what im really having trouble with

5. Sep 1, 2010

### Office_Shredder

Staff Emeritus
It says the average height of the tide is 3 meters. $$2 \sin(\frac{\pi}{6}x)$$ has an average height of 0 (it oscillates between -2 and 2). How much do you have to shift it up to get an average height of 3?

For the phase shift, what time is x=0 going to correspond to?

6. Sep 1, 2010

### laura11

would you shift it up 3?

7. Sep 1, 2010

### laura11

is the answer y=2sin(pi/6x) +3?

8. Sep 1, 2010

### laura11

yesss.. nooo?? haha

9. Sep 1, 2010

### Office_Shredder

Staff Emeritus
That could be right. The problem doesn't specify what time x=0 is at. So you get to pick. What time does x=0 represent?