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Lesson: 4.5 Graphs of Sine and Cosine Functions Part 2
Goal:
Graph Sine and Cosine Functions
DOD
Yesterday we talked about vertical stretches (change amplitude) and horizontal
stretches (change period).
Today we will look at horizontal and vertical shifts.
Graphs of Sine and Cosine Functions (p. 357 of text)
The graphs of
± ² ³´µ¶·¸ ¹ º» ¼ ½
and
± ² ¾¿³
¶
·¸ ¹ º
»
¼ À
have the following
characteristics (assume
· Á Â
).
Amplitude=
Ã
²
Ã
(if
² Ä Â
, then flip
across x-axis)
Period=
ÅÆÇ·
Horizontal Shift
Left and right endpoints
of one period
Solve for
¸
:
·¸ ¹ º ± Â
·¸ ¹ º ± ÅÆ
Vertical Shift
Oscillates around line
± ½
(if
½ ± Â
, then x-axis)
if
½ Á Â
, then shift up
if
½ Ä Â
, then shift down
For every function that I will graph, I will find those 4 things above in that order.
1)
amplitude
2) period
3) horizontal shift
4) vertical shift

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