Intro to Polar Coordinates Objectives: Be able to graph and convert between rectangular and polar...
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Transcript of Intro to Polar Coordinates Objectives: Be able to graph and convert between rectangular and polar...
Intro to Polar CoordinatesObjectives: Be able to graph and convert between
rectangular and polar coordinates. Be able to convert between rectangular and polar equations.
TS: Examine Information from more than one point of view.
Warm Up: If I were to turn 3π/4 degrees from the positive x-axis and then walk out 4 units from the origin in that direction, find the coordinates of the
point I would be standing on.
Polar Coordinate System
A point in the Polar
coordinate system
is (r, θ), where r is
the directed distance
from the pole and θ
is the directed angle
from the polar axis
Graphing Polar Coordinates
A (1, π/4)
B (3, - π/3)
C (3, 5π/3)
D (-2, -7π/6)
E (-1, 5π/4)
Conversions between rectangular and polar
Given (r, θ), the point (x, y) would be in the same location given all the following relations were true.
x = rcosθ r2 = x2 + y2
y = rsinθ tany
x
Graphing Polar Coordinates
(-√2, 3π/4)
Convert to Rectangle,
Graph both.
Use the conversions to change the given coordinates to their Polar Form
(-4, -4)
(-1, √3)
Converting/Graphing Equations
Polar to Rectangular
1) r = 2
Converting/Graphing Equations
Polar to Rectangular
2)θ = π/3
Converting/Graphing Equations
Polar to Rectangular
3) r = secθ
Converting/Graphing Equations
Rectangular to Polar
4) x2 + y2 = 16
Converting/Graphing Equations
Rectangular to Polar
5) y = x
Converting/Graphing Equations
Rectangular to Polar – Convert to polar form. Identify the figure and graph it. Confirm by graphing the polar as well on your calculator
6) x2 + y2 – 8y = 0
More Challenging Conversions
7) Polar to Rectangular
sec 3r
More Challenging Conversions
8) Rectangular to Polar
(x – 1)2 + (y + 4)2 = 17