1. Intro to Polar Section 10.7 Precalculus PreAP/Dual, Revised ©2017
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§10.7: Introduction to Polar Coordinates

2. §10.7: Introduction to Polar Coordinates
What is Polar Form?
The polar form of a complex number is another way to represent a complex number.
Polar Coordinates are two values that locate a point on a plane by its distance from a fixed pole and its angle from a fixed line passing through the pole
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§10.7: Introduction to Polar Coordinates

3. §10.7: Introduction to Polar Coordinates
Forms Introduced
Polar Coordinates: 𝒓, 𝜽
Rectangular/Standard Form: 𝒙, 𝒚
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§10.7: Introduction to Polar Coordinates

4. §10.7: Introduction to Polar Coordinates
Using Trigonometry
𝒙 = 𝒓 𝐜𝐨𝐬⁡𝜽
𝒚 = 𝒓 𝐬𝐢𝐧⁡𝜽
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§10.7: Introduction to Polar Coordinates

5. §10.7: Introduction to Polar Coordinates
Review
Plot 𝟑, 𝟔𝟎° on a regular graph.
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§10.7: Introduction to Polar Coordinates

6. §10.7: Introduction to Polar Coordinates
Example 1
Plot 𝟑, 𝟔𝟎° on a polar graph.
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§10.7: Introduction to Polar Coordinates

7. §10.7: Introduction to Polar Coordinates
Example 2
Plot 𝟑, − 𝟓𝝅 𝟔 on a polar graph.
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§10.7: Introduction to Polar Coordinates

8. §10.7: Introduction to Polar Coordinates
Example 3
Plot −𝟑, − 𝝅 𝟔 on a polar graph.
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§10.7: Introduction to Polar Coordinates

9. §10.7: Introduction to Polar Coordinates
Your Turn
Plot A −𝟐, 𝟓𝝅 𝟒 and B −𝟏, − 𝟑𝝅 𝟒 on a polar graph.
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§10.7: Introduction to Polar Coordinates

10. Identifying Multiple Representations of Points
With the argument or the angle
Add and/or subtract multiples of 𝟐𝝅 or 𝟑𝟔𝟎°
With the moduli or the “radius”
With a negative length, add and/or subtract multiples of 𝝅 or 𝟏𝟖𝟎°
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§10.7: Introduction to Polar Coordinates

11. §10.7: Introduction to Polar Coordinates
Recall
Plot 𝟑, 𝟔𝟎° on a polar graph. Are there other ways of labeling this point?
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§10.7: Introduction to Polar Coordinates

12. §10.7: Introduction to Polar Coordinates
Example 4
Plot the point of 𝟑, − 𝟑𝝅 𝟒 on a polar graph. Then, find three additional polar representations of this graph from −𝟐𝝅, 𝟐𝝅
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§10.7: Introduction to Polar Coordinates

13. §10.7: Introduction to Polar Coordinates
Example 5
Plot the point of −𝟓, − 𝟐𝝅 𝟑 on a polar graph. Then, find three additional polar representations of this graph from –𝟐𝝅, 𝟐𝝅
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§10.7: Introduction to Polar Coordinates

14. §10.7: Introduction to Polar Coordinates
Your Turn
Plot the point of 𝟐, 𝟑𝝅 𝟒 on a polar graph. Then, find three additional polar representations of this graph from −𝟐𝝅, 𝟐𝝅
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§10.7: Introduction to Polar Coordinates

15. §10.7: Introduction to Polar Coordinates
Assignment
Worksheet
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§10.7: Introduction to Polar Coordinates