The document discusses sine and cosine graphs, noting that they are similar but sine passes through the origin at (0,0) while cosine passes through (0,1). It defines key properties of the graphs including amplitude, period, phase shift, and vertical shift. Amplitude refers to half the total height or distance from the middle. Period is the length of one complete cycle. Phase shift slides the graph left or right while vertical shift moves it up or down. An example equation, Y = sin(4x - 2) + 3, is provided to demonstrate how these properties are represented in the function.

1. SINE AND COSINE
GRAPHS

2. These graphs are almost identical! One major
difference is where they start.
Y = Sin(x) passes through the origin (0,0)
Y = Cos(x) passes through (0,1). It has a peak at
the y-axis.

3. Amplitude.
Amplitude is similar to height. However,
remember, amplitude is measured from the
middle up. (or half the total distance)

4. Phase Shift.
Phase shift is sliding the entire graph left and right

5. Vertical Shift
Vertical Shift moves the entire graph up or down

6. Period
Period is the length of one complete cycle of the graph

7. All together…

8. The Equation
Amplitude
(height)
Period
P = 2π/B
(length)
Phase Shift
PS= - c/b
(left/right)
Vertical Shift
(up/down)

9. Y = sin(4x − 2) + 3
amplitude A = 2
period 2π/B = 2π/4 = π/2
phase shift −C/B = −(−2)/4 = 1/2
vertical shift D = 3