Transcript 8.3 Power Point

8.3 – Model Periodic
Behavior
Essential Question: How do
you write an equation for a
sin or cos graph?
General Sine Waves
(sin & cos):

If the graphs of y = A cos Bx and
y = A sin Bx are translated horizontally
h units and vertically k units, then the
resulting graphs have equations:

y – k = A sin B(x – h)

y – k = A cos B(x – h)
Pictures:
To find translation, use axis of
the wave:


Axis of the Wave – a horizontal
line midway between the
maximum and the minimum.
y = Max + Min
2
To find translation:
For Cosine:
- Count the translation amounts
(horizontally and vertically) from (0, A) to
the highest point on the curve.
For Sine:
- Count the translation amounts
(horizontally and vertically) from (0, 0) to
the point where the curve intersects the axis
of the wave (where curve is going up).
Example

Find the equation for the given graph.
- For Cosine:
- For Sine:
y
y
x
x
Example

What is the translation?

y – 2 = 2 cos 2 (x – 3)
 What is the translation?

y = -5 + 2 sin 2 (x + 1)
Example

Give an equation of the trig. graph.
Example

Sketch the graph of
y = 3 + 5 sin 2(x + 1)
Example
a) What is the amplitude?
b) What is the period?
Example
c) What is the axis of the wave?
d) Give an equation for the trigonometric
graph.