Aim: How do we sketch the graphs of y = asinx and y = acosx ?
HW # 27: p. 717 # 1­6, 7, 8, 9, 12, 15 ­ 18
Do Now: Use your calculator (if you have a graphing one) to graph each of the following on the same set of axes:
1) y = sinx
2) y = 2sinx
3) y = ½sinx
NOTE: Radian Mode
Use zoom TRIG
Or window:
Xmin = ­2π
Xmax = 2π
Ymin = ­2
Ymax = 2
May 3­9:17 AM
What differences/similarities are there for these three graphs?
y = 2sinx
y = ½sinx
y = sinx
2
1
2π
­2π
­3π/2
­π
­π/2
0
π/2
π
3π/2
­1
­2
period = 2π
DEF: The amplitude of a periodic function is the "height" of the curve from the x­axis to its highest point.
In general, for the functions y = asinx and y = acosx, the amplitude = | a |
May 3­9:26 AM
1
Now let's graph the following on our graphing calculators:
y = cosx
y = 4cosx
y = ­4cosx
y = 4cosx
y = cosx
y = ­4cosx
What changes when the "a" value (the number in front) is negative?
y= 4cosx
y = ­4cosx
May 3­9:38 AM
The graph of y = asinx looks like this when a is positive:
The graph of y = asinx looks like this when a is negative:
The graph of y = acosx looks like this when a is positive:
The graph of y = acosx looks like this when a is negative:
May 3­9:46 AM
2
State the amplitude and the range, and sketch the following:
Verify on a calculator.
a) y = 7sinx
b) y = 4cosx
c) y = ­½cosx
d) y = 5 sinx
e) y = ­3cosx
May 3­9:44 AM
f ) Sketch the graph of y = ­2 sin x on the interval [­π, 4π].
State the following:
amplitude:
frequency:
period:
1/4 period:
Feb 22­10:10 AM
3
Apr 24­12:03 PM
4