Topic: Descriptions of Special Polar Graphs

POLAR GRAPHS: PUTTING IT ALL TOGETHER N 18-5 Lines: θ = a rcosθ = a rsinθ = a

Circles: r = a r  acos r  asin

Cardioids and Limaçons: r  a  bcos r  a  bsin

Rose Curves: Lemniscates: r  acosn r  asinn r2  a2cos2

r2  a2sin2 N 18-5 1. When are polar graphs functions? For rectangular equations: Function: A relation in which ______. No x-value can be used twice with different y-values. Graph will pass the ______Test.  X is the ______(input)  Y is the ______(output)

For polar equations: Function: A relation in which ______.  ___ is the ______(input)  ___ is the ______(output)

2. Are the graphs on page 1 functions?

3. Do polar functions pass the Vertical Line Test?

4. Advantages of polar graphs over rectangular graphs:

Write the equation for each graph. 5. ______6. ______N 18-5 7. ______8. ______

9. The Spiral of Archimedes: r = aθ Make a table and graph:  r = 

r θ r θ 0 5  2 2 3π π 7 3 2 2 4π 2π

What happens to r as θ increases?

 Graph r = on your calculator. 