Trig Writing assignment: model the amount of perceived daylight in a certain location

[Revert]

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.

 

[stapel]

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?

Yes. You're in a trig class, and the exercise clearly states that "it is possible to use a sinusoidal function to model", so you're expected to create a sine function as the model.

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.

So you're going to have a sine function, and it's period will be one 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.

So what will be the minimum y-value of your sine wave? What will be the maximum y-value of the sine wave? What then will be the midline value? What then will be the amplitude?

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.

So they're starting the year at about the vernal equinox, or about halfway between the max and min values. So is there going to be any phase shift for your sine wave?

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.

Once you find your function, plug in "11" for "y", and solve for t. Then back-solve to find the actual days of the year. (There should be two.) Do the same for "15".

If you get stuck, please reply showing all of your work and reasoning, starting with your answers to the above questions. Thank you!