The water level varies from 12 inches at low tide to 52 inches at high tide. Low tide occurs at 9:15 a.m. and high tide occurs at 3:30 p.m. What is a cosine function that models the variation in inches above and below the water level as a function of time in hours since 9:15 a.m.?

Question

anonymous · Answer

Help please @dan815

anonymous · Answer

y=-20 cos(x) + 32 is what I got, is that right?

dan815 · Answer

the amp and the veritcal shift is right, currently your period is 2pi, meaning every 2pi hours it completes a cycle, is that what you want you want a period to last from 
9:15 am to 3:30 pm which is about 6 hours and 15 mins whoch is 6.25 hours so ya xD
i mean 2pi is pretty close but if you want be exact

dan815 · Answer

can you try to figure out what u must do to the period to get it to 6.25 exactly currently you are at 2pi which is 2*3.14... about 6.28 approximately

dan815 · Answer

remember how 
y=cos(8x) compressed the period by 8 times
how much do we have to compress or elongate the period this time to go from
2pi to 6.25