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Intro to Polar CoordinatesPowerPoint Presentation

Intro to Polar Coordinates

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## PowerPoint Slideshow about ' Intro to Polar Coordinates' - artaxiad-jacobs

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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

Experiment with Polar Function Spreadsheet

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

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