pc c4 s5 blank notes ­ all transformations.notebook
Sec 4.5
Graphs of the Sine and Cosine Functions
Domain: All Real numbers
(radians or degrees)
Range:
Domain: All Real numbers
(radians or degrees)
Range:
pc c4 s5 blank notes ­ all transformations.notebook
Characteristics of Trig Functions
­ all trig functions repeat themselves, the horizontal distance it takes for the graph to repeat itself is called the period.
­ the sine and cosine functions have an amplitude. It is defined as half the distance between the maximum and minimum values.
For the basic sine function
period =
amplitude = For the basic cosine function
period = amplitude = pc c4 s5 blank notes ­ all transformations.notebook
Transformations
amplitude
= phase shift
= period
d = vertical shift
bx ­ c : shift right
positive : shift up
bx + c : shift left
negative : shift down
the left and right endpoints of a one­cycle interval can be found by solving the two equations:
left endpoint: bx ­ c = 0
right endpoint: bx ­ c = 2
pc c4 s5 blank notes ­ all transformations.notebook
Example Identify the amplitude,period, phase shift, and vertical shift
amplitude
period
phase shift
A)
B)
C)
Example Identify the amplitude,period, phase shift, and vertical shift. Then graph.
vertical shift
pc c4 s5 blank notes ­ all transformations.notebook
Example Identify the amplitude and period from the equations
The sine & cosine graphs can be changed to any size wave by changing some things in the equation. ­ these variables do the same thing to the sine and cosine graphs
d = vertical shift