### 4.1.4 Shifts of Sine & Cosine

```Today you will use shifts and vertical stretches to graph and
find the equations of sinusoidal functions. You will also
learn the 5-point method for sketching graphs.
 What does the “normal” sine graph look like?
What does the “normal” cosine graph look like?
Sine Wave Tracer
 Draw the “normal” graph for each. Label the 5 key




points.
Maximum? Minimum? Crossings?
Period? Amplitude?
Parent Equation
General Equation
P arent E quation: y  sin x
G eneral E quation: y  a sin( b ( x  c ))  d
Period: 2π
Amplitude: 1
Maximum: (
Minimum:

(
,1)
2
3
,  1)
2
Crossings: (0, 0) ( , 0) (2  , 0)
P arent E quation: y  cos x
G eneral E quation: y  a cos( b ( x  c ))  d
Period: 2π
Amplitude: 1
Maximum:
(0,1) and (2  ,1)
Minimum:
Crossings:
( ,  1)
(

2
, 0) (
3
2
, 0)
Reflect over x-axis
y   A sin B  x  C   D
Vertical Stretch/ Shrink
Left/ Right
Up/Down
Horizontal Stretch/ Shrink
Complete
4-49 & 4-50 with your
partner.
Complete
4-52 parts b, c, and d