Polar Coordinates Lesson 10.5

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)

Plot Given Polar Coordinates Locate the following

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

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

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

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

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

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

Graphing Polar Equations Set Zoom to Standard,  then Square

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

Assignment Lesson 10.5A Page 433 Exercises 1 – 45 odd Lesson 10.5B Page 433 Exercises 47 – 61 odd