Review graphing reciprocal functions, graphing absolute value functions, introduction to trigonometric modeling.

1. What do the planets have to
do with trigonometry?

2. sketch the graph of , that is
Given

3. Sketching the graphs of absolute value functions ...
How to sketch: y = |ƒ(x)|
Definition of Absolute Value
Step 1: Sketch the graph of y = ƒ(x).
Step 2: Reflect all the part of the line
that is below the x-axis over the x-axis.
y=x
y = |xl

4. Sketch the graph of

5. sketch the graph of
Given

6. What Transformations Do You See?

7. Trigonometric Modeling and Transformations
An Example
For a Saskatchewan
town the latest sunrise is
on Dec 21 at 9:15 am.
The earliest sunrise is on
June 21 at 3:15 am.
Sunrise times on other
dates can be predicted
using a sinusoidal
equation. Morning at Swiftcurrent Lake
Note: There is no daylight savings time in Saskatchewan.
a) Sketch the graph of the sinusoidal function described above.
b) Write 2 equations for the function; one using sine the other cosine.
c) Use one of the equations in (b) to predict the time of sunrise on April 6.
d) What is the average sunrise time throughout the year?
e) On what days will the sunrise at 7:00am?