Creating a sinusoidal model using temperature v days of the year

•Topic: Sinusoidal functions

Aim: How can we use the graphing calculator to find the model of a sine function?

•

•Write the equation of a sine function with a >0, amplitude 7.85, and cycles .016 in 2π  

•The sine function with shifts

•Y = A sin (Bx + C) + D

•

•A = amplitude

•B = cycles in 2π

•C = horizontal shift

•D = vertical shift

•

•Look at problem 27 on pg 368 handout

•Modeling temperature on several days of the year

•Graph the model

•Y1 = = 7.85 sin(.016x – 2.22) + 82.19

•

•Fix the WINDOW for domain and range

•

•GRAPH

•

•Sketch the graph on the xy plane

•Extending your thinking

•How could we use the sine model to write the cosine model?

•

•Recall how we shift from sine to cosine (by π/2)

•

•Graph the cos model on the same set of axes

•Horizontal translations – phase shifts
g(x): horizontal translation of f(x)
g(x) = f (x – h)

•Important consideration

•The value of h f (x – h):

•

•If h > 0, the shift is to the right

–Example: f ( x – 3 ) is a horizontal shift 3 units to the right

•If h < 0, the shift is to the left.

–Example: cos (x + 4) = cos (x – (-4)), h = -4; the shift is 4 units to the left

•Vertical translations
h(x): vertical translation of f(x)
h(x) = f(x) + k

•Exit slip

•What are the major differences between the cosine and the sine functions?

•