Intro to Polar Coordinates Lesson 6.5A

2 Points on a Plane  Rectangular coordinate system Represent a point by two distances from the origin Horizontal dist, Vertical dist  Also possible to represent different ways  Consider using dist from origin, angle formed with positive x-axis r θ (x, y) (r, θ)

3 Plot Given Polar Coordinates  Locate the following

4 Find Polar Coordinates  What are the coordinates for the given points? B A C D A = B = C = D =

5 Converting Polar to Rectangular  Given polar coordinates (r, θ) Change to rectangular  By trigonometry x = r cos θ y = r sin θ  Try = ( ___, ___ ) θ r x y

6 Converting Rectangular to Polar  Given a point (x, y) Convert to (r, θ)  By Pythagorean theorem r 2 = x 2 + y 2  By trigonometry  Try this one … for (2, 1) r = ______ θ = ______ θ r x y

7 Polar Equations  States a relationship between all the points (r, θ) that satisfy the equation  Exampler = 4 sin θ Resulting values θ in degrees Note: for (r, θ) It is θ (the 2 nd element that is the independent variable Note: for (r, θ) It is θ (the 2 nd element that is the independent variable

8 Graphing Polar Equations  Set Mode on TI calculator Mode, then Graph => Polar  Note difference of Y= screen

9 Graphing Polar Equations  Also best to keep angles in radians  Enter function in Y= screen

10 Graphing Polar Equations  Set Zoom to Standard, then Square

11 Try These!  For r = A cos B θ Try to determine what affect A and B have  r = 3 sin 2θ  r = 4 cos 3θ  r = sin 4θ Experiment with Polar Function Spreadsheet Experiment with Polar Function Spreadsheet

12 Assignment A  Lesson 6.5A  Page 424  Exercises 1 – 47 odd

Polar Coordinates Lesson 6.5B

14 Write Polar Equation in Rectangular Form  Given r = 2 sin θ Write as rectangular equation  Use definitions And identities (see inside back cover)  Graph the given equation for clues

15 Write Polar Equation in Rectangular Form  Given r = 2 sin θ We know Thus And

16 Write Rectangular Equation in Polar Form  Consider 2x – 3y = 6 As before, use definitions

17 Assignment B  Lesson 6.5B  Page 424  Exercises 49 – 73 odd