Lesson 10 – 1 Polar Coordinates

Lesson 10 – 1 Polar Coordinates Pre-calculus

Learning Objective • To graph polar coordinates • To convert polar coordinates to rectangular coordinates • To convert rectangular coordinates to polar coordinates

The Cartesian system of rectangular coordinates is not the only graphing system. This chapter explores the polar coordinate system. Polar Coordinates We will graph in what is called the -plane IMPORTANT!!! (r, ) P r fixed ray (polar axis) fixed point (pole or origin) A polar coordinate is the ordered pair (r, ) r = distance from pole to point = angle from polar axis (deg or rad) (pos or neg) on terminal side (pos or neg) on opp of terminal side clockwise counterclockwise

Graph each point on plane. (Just sketch) Polar Coordinates 1. P 2. Q

Graph each point on plane. (Just sketch) Polar Coordinates 3. R

4. Plot Polar Coordinates 1 Which of these does NOT represent the same point? (Identify & FIX IT!)  A. or B. C. Or many more!

Note: Since and , will produce equal angles, a point can be represented in infinitely many polar coordinate pairs. Polar Coordinates can also be positive or negative, adding to the options Note: If and , then represents exactly 1 point.

Discuss • Talk to your neighbor • - Summarize what we just did! • - What do you know how to do now? • - What type of questions will be asked?

An equation with polar coordinates is a polar equation. We will graph with constants today, and , and explore more complicated ones tomorrow. Polar Equation can also be positive or negative, adding to the options 5. Graph the polar equation (length always 3, angle is anything) 1 2 3

6. Graph the polar equation *Same as Polar Equation 1 2 3 4

7. Graph the polar equation Polar Equation (angle always can be anything positive or negative) OR

8. Graph the polar equation Polar Equation (angle always can be anything positive or negative)

If we superimposed the rectangular coordinate system on theplane we can discover their relationships. Polar Equation In Cartesian/ rectangular: (x, y) (r, ) IMPORTANT!!! r y x You will use these relationships to change equations from one system to another system.

To convert from polar to rectangular: Polar Coordinates VERY IMPORTANT!!! To convert from rectangular to polar: If If

Quick Refresher… • - What’s the exact value of ? • - What’s the exact value of ? 1st Semester.. Trig…

Find the rectangular coordinates. Rectangular Coordinates 9.

Find the rectangular coordinates. Rectangular Coordinates 10.

Find the rectangular coordinates. Round to the nearest hundredth if necessary. Rectangular Coordinates 11. (not famous – use calculator) ***RAD mode

12. Find polar coordinates of Polar Coordinates  13. Find polar coordinates of 

14. Convert to a polar equation Polar Coordinates 15. Convert to a polar equation

16. Convert to a rectangular equation Polar Coordinates Multiply both sides by r 17. Convert to a rectangular equation Square both sides.

18. Convert to a rectangular equation Polar Coordinates FIND ANOTHER WAY TO SOLVE! y 19. Convert to a rectangular equation Take the tangent of both sides

20. Convert to a rectangular equation Polar Coordinates 21. Convert to a rectangular equation OTHER WAYS TO SOLVE!

Assignment Pg. 492 #1–29 odd (skip 7 & 15), 22, 34, 35, 37, 41, 43, 45, 49, 51

What is the coordinate of the graph shown? Check – up 1.

What is the coordinate of the graph shown? Check – up 2.

Find the rectangular coordinates. Round to the nearest hundredth if necessary. Check – up 3.

4. Find polar coordinates of Check – up

5. Convert to a rectangular equation Check – up

Lesson 10 – 1 Polar Coordinates