Trigonometry
posted by Fred on .
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.

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= (111)/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