Sinusoidal phase shift - 04/09//13

Topic: Sinusoidal functions

Aim: How can we represent a horizontal shift of the sine function?

Do Now: Sketch a sine curve with an amplitude of 1 and a period of 2π.

Analyzing the basic sine curve

In your sketch:

a) identify the maximum value

b) identify the minimum value

c) identify the ‘three’ zeros

　

Modeling a horizontal shift

y = sin x              y = cos x

Horizontal shift – phase shift

The graphs of sine and cosine are the same when sine is shifted left by

π/2. Such a shifting is referred to as a horizontal shift (or phase shift).

Shift sine to the left to create cosine.

(Shift cosine to the right to create sine)

On your own

Start with your sketch of y = sin x

Shift to the left by

π/2 and sketch a basic cos curve (use a different color)

Your sketch should resemble diagram in previous slide.

Analyzing the basic cos curve

In your sketch:

a) identify the maximum value

b) identify the minimum value

c) identify the zeros (how many are there?)

Equivalent sinusoidal function

　

Analysis

If the horizontal shift is positive, the shifting moves to the right.  If the horizontal shift is negative, the shifting moves to the left.  

y = A sin( B (x -C) ) + D

From the sinusoidal equation above, the horizontal shift is obtained by determining the change being made to the x value. The horizontal shift is C.

Note: when C is negative, the shift is right and when C is positive, the shift is left

Exit slip

If you graph the basic sine function, y = sin x and then graph y = sin (x +

π/2), how will it transform?

What kind of shift has occurred?

Can you predict what a vertical shift might look like?