Polar and Rectangular Coordinates

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Polar and Rectangular Coordinates

• Section 9-3

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Polar to Rectangular Coordinates

• (r, ?) ? (x, y)
• x rcos?
• y rsin?
• Example (-3, p/3)
• (-3/2, -3v3/2)
• Example (10, - 40)
• (7.7, -6. 4)

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Rectangular to Polar Coordinates

• (x, y) ? (r, ?)
• r v(x2 y2)
• ? tan-1(y/x)
• Make sure you know what quadrant ? is in!
• Example P(- 4, 8)
• r v80 8.9
• tan-1 (8/-4) -63.4
• ? 116.6
• (8.9, 116.6)

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Equations Expressed in Polar Form

• Example 1
• x2 y2 100
• r2 100
• r 10

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Example 2

• x 3
• rcos ? 3
• r 3/cos ?

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Example 3

• y -10
• rsin ? -10
• r -10/sin ?

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Example 4

• 2x2 2y2 5y
• 2(x2 y2) 5(rsin?)
• 2r2 5rsin?
• 2r 5sin?
• r (5/2) sin?

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Express in Rectangular Form

• Example 1
• r -3
• r2 9
• x2 y2 9

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Example 2

• r 10 . 5cos? 8sin?
• r(5cos? 8sin?) 10
• 5rcos? 8rsin? 10
• 5x 8y 10

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Homework

• P.486 15-25odd, 26-36even