Trigonometric Functions Applications

[Borislv5]

Hello, I've missed a bit of class because of being sick and when I returned we started doing trigonometric functions. I'm not exactly sure how to go about this. I will gladly accept explanations and formulas, but the question goes like this:

The number of daylight hours, D, in the city of Worcester, Massachusetts, where x is the number of days after January 1 (0_<x_<365) may be calculated by the function D(x)=3sin 2pi/365 (x-78)+12

I'm guessing the -78 and +12 part is the transformations done, but the questions also say this:
Find the period, amplitude, horizontal shift, phase shift, vertical shift, and how many hours of sunlight there will be on February 21st of any year.

Thanks for the help!

 

[Deleted member 4993]

Hello, I've missed a bit of class because of being sick and when I returned we started doing trigonometric functions. I'm not exactly sure how to go about this. I will gladly accept explanations and formulas, but the question goes like this:

The number of daylight hours, D, in the city of Worcester, Massachusetts, where x is the number of days after January 1 (0_<x_<365) may be calculated by the function D(x)=3sin 2pi/365 (x-78)+12

I'm guessing the -78 and +12 part is the transformations done, but the questions also say this:
Find the period, amplitude, horizontal shift, phase shift, vertical shift, and how many hours of sunlight there will be on February 21st of any year.

Thanks for the help!

What would be a generic sine (wave) function that includes - period, amplitude and phase shift?

Please show us what you have tried and exactly where you are stuck.​

​

Please follow the rules of posting in this forum, as enunciated at:​

​

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520​

​

Please share your work/thoughts about this problem.​

 

[Steven G]

Suppose y = A * sin(Bx - C) + D ............or............ y = A * cos(Bx-C) + D
The amplitude = |A|
horizontal phase shift is C/B
vertical shift is D
Period = 2pi/|B|
Now try to figure out why I am correct (or incorrect)