Posted by **Fred** on Sunday, August 15, 2010 at 9:36pm.

At the ocean, it is known that the tide follows a trigonometric path. At high tide,

the water comes in to a point 1 meter from where I placed a flag. At low tide, the

water comes in to a point 11 meters from the same flag. The time it takes from to

get from high tide to low tide is 5 hours. It is now midnight and it is high tide.

(Note: low tide=max and high tide=min in this case)

Plot the motion for two complete cycles and state a possible equation for this motion.

I have absolutely no idea where to even begin with this problem, other than the equation involves either sin(x) or cos(x). Any tips on where to start or help working out how to do this word problem would be much appreciated.

- Trigonometry -
**bobpursley**, Sunday, August 15, 2010 at 10:13pm
assume it is

distance=Asin(wt+theta) + k

low tide:

11=Asin(w5+theta)+k

high tide

1=Asin(0+theta)=k

but you also know that that at t=5, half a cycle has occured, to A= (11-1)/2

high tide:

1=5sin(theta)+k

low tide

11=5sin(PI + theta) + k

but sin(PI+theta)=-sinTheta so

11=-5sinTheta +k

add the equations for high tide and low tide

12=2k k=6

subtract the equations

10=10sinTheta

theta= PI/2

so you have theta, A, k

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