1. Pre-Calculus
Unit 2 Day 5

2. HW Questions

3. Next
Continuation of yesterday’s notes/topic

4. Referring to yesterday’s notes, what do the graphs of the following look like.
Can you think of another equation that would result in the same graph?
Can you think of two other equations that would result in the same graph?

5. What would the graph of these pairs of equations look like?

6. How about this pair ?

7. NEW MATERIAL Polar vs Cartesian Unit 8 Day 5
Pre-Calculus
NEW MATERIAL
Polar vs Cartesian
Unit 8 Day 5

8. It is good to have a Cartesian coordinate system AND a Polar coordinate system because some functions are easier in Cartesian and some are easier in Polar:

9. Recall from yesterday r q

10. Same point but different coordinate system . . .x

11. Converting from polar to Cartesian:
Example:
Convert to Cartesian coordinates : r q

12. Now, YOU try!!
Convert into Cartesian:

13. Converting from Cartesian to Polary
Example:
Convert to Polar Coordinates
Finding r:
Finding  is more involved . . . x

14. Finding  . . . . Example: Convert to Polar Coordinates
Now we have to pair up the r and  . . .

15. Pairing up r and  . . .
The original Cartesian coordinates place the point in the 2nd quadrant. So

16. The Cartesian point in Polar form is:
There are multiple conversions to polar! 
Being in the correct location when finished with the conversion is what is important.

17. Up Next . . .
Converting points that would not have a  landing on a known location on the unit circle

18. Convert to Polar Coordinates
This is in the first quadrant.
To end up in the 3rd quadrant, the location of the given point, we would need
The other possibility would be to add to the angle and use the positive value of r.

19. Practice: Convert into Polar Coordinates

20. Recap
Cartesian to Polar r y
Polar to Cartesian q x

21. Converting EQUATIONS from Polar to Cartesian
Confirm your answer by graphing the original polar equation to see that it is a vertical line at x=-3

22. Confirm your answer by graphing the original polar equation to see that it is a line equivalent to y=5+2x