Polar Coordinates
description
Transcript of Polar Coordinates
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
2,4
A
33,2
C
24,3
B
51,4
D
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
2,4
A
Converting Rectangular to Polar
• Given a point (x, y) Convert to (r, θ)
• By Pythagorean theorem r2 = x2 + y2
• By trigonometry
• Try this one … for (2, 1) r = ______ θ = ______
•
θ
r
x
y
1tan yx
Polar Equations
• States a relationship between all the points (r, θ) that satisfy the equation
• Example r = 4 sin θ Resulting values
θ in degrees
Note: for (r, θ)
It is θ (the 2nd 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 keepangles 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 = 2 + 5 sin 4θ
Assignment
• Lesson 10.5A• Page 433• Exercises 1 – 45 odd
• Lesson 10.5B• Page 433• Exercises 47 – 61 odd