January 24 th copyright2009merrydavidson. y = cos x.

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Presentation transcript:

January 24 th copyright2009merrydavidson

y = cos x

y = D - A trig function B (  + C) Horizontal shift “C” units “right or left” Affects x-values Determines the period. Affects x-values Amplitude Affects y-values Vertical shift Affects y-values Negative sign means reflect over the x-axis

AMPLITUDE Is the Positive height of the trig graph. y = D - A trig function B (  + C)

What is the amplitude of the sine parent graph? 1 At the origin, middle, high, middle, low.

y = cos x What is the amplitude of the cosine parent graph? 1 At the origin, high, middle, low, middle.

On your class worksheet Fill in the amplitude for all 10 equations.

PHASE SHIFT:Horizontal (L or R) The start point has shifted pi/2 to the right. y = D - A trig function B (  + C)

On your class worksheet Fill in the phase shift for all 10 equations. Phase shift is always “inside” of the parenthesis.

VERTICAL SHIFT: up or down Now the start point is at y=2. The sine curve shifted up 2. y = D - A trig function B (  + C)

On your class worksheet Fill in the vertical shift for all 10 equations. Vertical shift is in the front or the back. Be careful with signs!

y = D - A trig function B (  + C) Will this be graphed in degrees or radians? degrees Use x for radians and theta for degrees.

PERIOD:Length of 1 cycle (when you get back to the start position.) PERIOD for sine and cosine parent function is 360 o or 2 pi radians. When you put transformations on the parent function the period changes.

PERIOD: How long it takes to repeat the pattern. (get back to the start position) It took Pi units to get back to the middle. So the period of this graph is pi.

You use “B” to find the period of the transformed function. y = D - A trig function B (  + C)

On your class worksheet Fill in the Period for all 10 equations.

Write an equation for a positive sine curve with an amplitude of 3, period of 90  and phase shift of 45  right. Start with the equation… y = D + A trig function B (  + C) Amplitude of 3 does what? 3 Our trig function is sine. y = sin  Phase shift now ( - 45) Period of 90. 4

Write a possible equation for a positive cosine curve with an amplitude of 4, period of 4 , and phase shift of  /2 right. Start with the equation… y = D + A trig function B (  + C) Amplitude of 4 does what? 4 Our trig function is cosine. y = cos x Phase shift now ( -  /2) Period of 4 . 1/2

HW: WS 7-1