Sine Modeling Project

Sunrise Data of Fenwick Island, Delaware

Finding the vertical translation

• Add the maximum and minimum and divide by 2.
• (7.3+4.63)/2=5.965
• y=sin x + 5.965

Finding the amplitude

• Take the maximum-minimum and divide by 2
• (7.3-4.63)/2 = 1.335
• y=1.335 sin x + 5.965

Finding the Period

• It takes 12 months for the sunrises to complete one cycle. So to find 'b', we use the equation 12 = 360/b
• b = 30
• y = 1.335 sin (30x)+5.965

Now I need to shift the graph approximately 2 units to the left.

Horizontal Translation

• I have to move the function to the left, so I set up the equation 2 = c/30; c = 60
• y = 1.335 sin (30x + 60) + 5.965

y=1.335sin(30x+60)+5.965