Sin and Cos Graphs
y=sin(x)
y = -sin(x)
y=cos(x)
y = -cos(x)
General Form of
Sinusoids
y = acos[b(x-h)] + k
y = asin[b(x-h)] + k
Amplitude (a)
The distance from the center of the graph to the maximum height, or
from the center to the minimum depth, or the AVERAGE (MEAN) of
the distance BETWEEN the maximum height and the minimum depth.
Frequency (b)
The number of period(s) in a 2π interval. b = 2π/period
Period (2π/b)
The length of one complete cycle. Period = 2π/b
Locator (x): h
The x value of the locator point. To find the y value of the locator
point, refer to the parent graph (+cos, -cos, + sin, -sin)
Midline: k
The middle of the sin or cos graph.
How do you
create an
equation (sin or
cos) from a
graph?
1.
Find the midline (k)
2. Find the amplitude (a)
3. Find the x-value of the locator point (h)
4. Find the period and then the value of b.
5. Write the equation so the locator point defines the sin/cos
function.
Example: Write
the equation for
this graph.
1.
Graphing a
sinusoid from an
equation in
general form.
Find k. Draw a dashed line at y=k.
2. Find a. Draw top and bottom guidelines (dashed) a units above
and below the midline, k.
3. Use the parent graphs to determine shape (sin, -sin, cos,-cos).
Start with h as starting point.
4. Plot the last point using the period, 2π/b. Then plot the middle
point, the ¼ point and the ¾ point (5 points total).
5. Draw a smooth curve and extend it for one more period.
Ex: Graph
y=-2cos[π/2 (x-3)]+1
a=
b=
period =
h=
k=