In the month of September, Shinobi is sent on an independent mission to recover lost treasure in a cavern embedded in a cliff. The cavern itself overlooks a vast ocean and the cliff is inaccessible due to its height of 53 feet.
As a ninja, Shinobi observes the nature around him. He realizes that every month relative to the moon, there are Spring (high) tides and Neap (low) tides that occur twice respectively. Spring tides occur when there is a full moon and new moon whereas neap tides occur at the quarter moon phases. In past recordings of the village, Shinobi notes that the Spring tides reached an average of 60 feet and that the Neap tides reach an average height of 23 feet in the past. He realizes that in order to reach the cavern, he needs to ride the high tide.
With the Moon going through its phases every month, when can Shinobi predict that the spring tide will come using the provided information.
Last quarter 9/04 NT
New moon 9/11 ST
1st quarter 9/18 NT
full moon 9/25 ST
a. Write a sine and cosine equation to represent the relationship between the tides.
b. In order to reach the cavern, Shinobi has to reach a height of 53 feet. At what dates during September would the tide be at this ideal height? Round your answer to the nearest day.
c. How long will the tide be over 53 feet? Round your answer to the nearest day.
