intro to polar coordinates
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Intro to Polar Coordinates. •. θ. r. 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. (x, y). •.

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Presentation Transcript
points on a plane

θ

r

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

(x, y)

(r, θ)

plot given polar coordinates
Plot Given Polar Coordinates
  • Locate the following
find polar coordinates
Find Polar Coordinates
  • What are the coordinates for the given points?

• A

  • A =
  • B =
  • C =
  • D =

• B

• D

• C

converting polar to rectangular
Converting Polar to Rectangular
  • Given polar coordinates (r, θ)
    • Change to rectangular
  • By trigonometry
    • x = r cos θy = r sin θ
  • Try = ( ___, ___ )

r

y

θ

x

converting rectangular to polar
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 = ______

r

y

θ

x

polar equations
Polar Equations
  • States a relationship between all the points (r, θ) that satisfy the equation
  • Example r = 4 sin θ
    • Resulting values

Note: for (r, θ)

It is θ (the 2nd element that is the independent variable

θ in degrees

graphing polar equations
Graphing Polar Equations
  • Set Mode on TI calculator
    • Mode, then Graph => Polar
  • Note difference of Y= screen
graphing polar equations1
Graphing Polar Equations
  • Also best to keepangles in radians
  • Enter function in Y= screen
graphing polar equations2
Graphing Polar Equations
  • Set Zoom to Standard,
    • then Square
try these
Try These!
  • For r = A cos Bθ
    • Try to determine what affect A and B have
  • r = 3 sin 2θ
  • r = 4 cos 3θ
  • r = 2 + 5 sin 4θ

Experiment with Polar Function Spreadsheet

write polar equation in rectangular form
Write Polar Equation in Rectangular Form
  • Given r = 2 sin θ
    • Write as rectangular equation
  • Use definitions
    • And identitiesGraph the given equation for clues
write polar equation in rectangular form1
Write Polar Equation in Rectangular Form
  • Given r = 2 sin θ
    • We know
    • Thus
    • And
write rectangular equation in polar form
Write Rectangular Equation in Polar Form
  • Consider 2x – 3y = 6
    • As before, usedefinitions
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