translating sinusoidal functions

•Full period examination: Tuesday April 23

•Sine curve & Cosine curve

•Amplitude

•Period

•Range

•Sketching

•Solving sinusoidal equations

•Tides and temperature problems

•Writing the sinusoidal equation

•Topic: Sinusoidal functions

Aim: How can we graph the translations of sinusoidal functions?

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•Write an equation of a sine function with a >0, amplitude 2, and period π  

•Translating sine and cosine functions

Essential Understanding:

You can translate periodic functions in the same way that you translate other functions.

•You can graph f (x –h) by translating the graph of f by |h| units horizontally.

•You can graph f(x) + k by translating the graph of f by |k| units vertically.

•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):

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•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

•Got it?

•What is the value of h in each translation?

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•Describe each phase shift (use a phrase such as 3 units to the left).

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• a. g(t) = f(t – 5)

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• b. y = sin (x + 3)

•Graphing translations

A. y = sin x + 3

• k = 3

•Translate the graph of the parent function 3 units up

B.y = sin ( x – π/2)

  Translate the graph of the parent function π/2 units to the right

•Exit slip

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

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