T = period = 12 hr
d(t) = 6 + 2 cos (2 pi t /12 - phase )
max at t = 4, so when t = 4 we want :
(2 pi t /12 - phase ) = 0
because cos 0 = 1, the max
2 pi * 4/12 = phase
phase = 8 pi/12 = 2 pi/3
so
d(t) = 6 + 2 cos ( pi t /6 - 2 pi/3 )
so put in 5 for d
-1/2 = cos ( pi t /6 - 2 pi/3 )
cosine of what 2 angles = -1/2 ?
The average depth of water at the end of a dock is 6 feet. This varies 2 feet in both directions with the tide. Suppose there is a high tide at 4 AM. If the tide goes from low to high every 6 hours, write a cosine function d(t) describing the depth of the water as a function of time with t = 4 corresponding to 4 AM. At what two times within one cycle is the tide at a depth of 5 feet?
2 answers
by the way,stick to radians, not degrees :)
1 answer