If we add a constant
c
to the argument
θ
within a trigonometric function, then
every measure of an angle
θ
is increased by
c
. Addition of
c
will shift the
function left or right. A
c
> 0 will shift the function to the left while a
c
< 0 will
shift the function to the right.
If we combine both the multiplication by a constant
k
and the addition of a
constant
c
to the argument
θ
(sin (
k
θ
+ c)), then the movement of the function
left or right with respect to the period change is called the phase shift. The
value for this shift is . A
c
> 0 will shift the function units to the left while a
c
< 0 will shift the function units to the right.
Calculator Operations
To investigate changes in amplitude, you will use the SHIFT/CHANGE feature of
the graphing calculator. Press 2ndF SHIFT/CHANGE , touch
B CHANGE
, and
double touch
5 Y=sin X
. Double touch the screen at
Y = 3
, above the box with
the arrows. Notice the new function Y = 3 sin X is displayed. Press ENTER to
place the new function in the list.
Double touch the screen at Y = -2, below the box with the arrows. Notice the
new function Y = -2 sin X is displayed. Press ENTER to place the new function
in the list.
Amplitude, Period, and Phase Shift/TRIGONOMETRY USING THE SHARP EL-9600
15
-
c
k
c
k
c
k
