Hey everyone. So my teacher gives out writing assignments in his class and I'm totally stumped. This section of my assignment includes sinusoidal functions, but I don't know what formula I'm suppose to create, but I'm guessing my formula has SIN in it? Please help.
Here's my assignment:
Trigonometric Stuff: It is possible to use a sinusoidal function to model the amount of perceived daylight in a certain location over the course of a year. For our city of Portland, Oregon, there is a minimum of 9 hours of “daylight” on the 1st day of winter and a maximum of 17 hours of “daylight” on the 1st day of summer. Let D represent the number of hours of “daylight” in Portland, Oregon, T days after the 1st day of spring (i.e T = 0 corresponds to March 20th). You may assume that 1 year has 365 days.
Find a formula for such a function, being sure to explain the practical meanings of any important pieces of the formula (amplitude, midline, and period). Use your formula to determine on what days of the year (month and day, not just T’s value) Portland has about 11 hours of “daylight” and about 15 hours of “daylight”. Please round to the nearest day, if not exact.
Here's my assignment:
Trigonometric Stuff: It is possible to use a sinusoidal function to model the amount of perceived daylight in a certain location over the course of a year. For our city of Portland, Oregon, there is a minimum of 9 hours of “daylight” on the 1st day of winter and a maximum of 17 hours of “daylight” on the 1st day of summer. Let D represent the number of hours of “daylight” in Portland, Oregon, T days after the 1st day of spring (i.e T = 0 corresponds to March 20th). You may assume that 1 year has 365 days.
Find a formula for such a function, being sure to explain the practical meanings of any important pieces of the formula (amplitude, midline, and period). Use your formula to determine on what days of the year (month and day, not just T’s value) Portland has about 11 hours of “daylight” and about 15 hours of “daylight”. Please round to the nearest day, if not exact.