Intro to Polar Coordinates

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# Intro to Polar Coordinates - PowerPoint PPT Presentation

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

### 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)

(r, θ)

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

• A

• A =
• B =
• C =
• D =

• B

• D

• C

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

• 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
• 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
• 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 Bθ
• Try to determine what affect A and B have
• r = 3 sin 2θ
• r = 4 cos 3θ
• r = 2 + 5 sin 4θ

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 Form
• Given r = 2 sin θ
• We know
• Thus
• And
Write Rectangular Equation in Polar Form
• Consider 2x – 3y = 6
• As before, usedefinitions