I decided to focus this mathematical exploration on the mathematics behind ocean tides. I started by examining the generic possibilities exposed by my teacher. Among them was the idea of ​​mathematics being applied to water. During my first search, I didn't find anything that seemed interesting, but I wanted to stick to the broad topic of water. After continued research, I decided to focus on a topic important to me: the ocean, specifically ocean tides. Every year my family takes a trip to California for a week at the beach and ever since I was little I was perplexed by the idea of ​​the water rising on the beach at night and receding during the day. As I got older, I learned that this movement was called tide and was caused by the gravity of the moon and sun affecting the ocean. So I decided to use the exploration as an opportunity to deepen my knowledge on this subject and tides became my subject for this. So I decided to explore the geographic and gravitational effects on tides as well as solar and lunar tides and finally predict the tides. For 39% of Americans living in oceanfront counties, tides are forces of nature that many people face every day. But what do we know about the tides? We know that tides are the rise and fall of ocean levels due to the gravitational pull of the sun and moon. There are also generally four tides per day, two lunar tides and two solar tides. In order to explore tides, one must first deduce the big ideas necessary to understand them. These include factors that can affect tides, such as the geography of an area and gravitational pull. A separate examination of solar and lunar tides will also be carried out. Finally, tide predictions will be taken into account... middle of paper ...... the highest and lowest tides occur when h'(t)=0. Thanks to this we can predict that the lowest tide of the first week has occurred. at t_min= 124.58 hours and h(t_min) = −0.86 feet. This predicts that there will be a low tide at 4:35 a.m. on September 6 of -0.86 feet. Actual low tide occurred at 3:35 a.m. on September 6. 6 by -1.0 ft. The forecast was off by 60 minutes and 0.14 feet. Using the same process we can predict the highest tide of the first week. Here we get the maximum occurring at t_max= 142.56 hours and h(t_max) = 6.40 feet or on September 6 at 10:33 p.m. with a height of 6.4 feet. The actual tide is 6.7 feet at 9:36 p.m. in September. 6. This time we were 0.3 feet down and 57 minutes late. This model was found not to be 100% accurate, however, only 4 cosine functions were used to predict tides while most models use up to 12 and the addition of more functions and parameters would create more accurate predictions..