Intro to Polar Section 10.7 Precalculus PreAP/Dual, Revised ©2017 viet.dang@humbleisd.net 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§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 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§10.7: Introduction to Polar Coordinates Forms Introduced Polar Coordinates: 𝒓, 𝜽 Rectangular/Standard Form: 𝒙, 𝒚 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§10.7: Introduction to Polar Coordinates Using Trigonometry 𝒙 = 𝒓 𝐜𝐨𝐬⁡𝜽 𝒚 = 𝒓 𝐬𝐢𝐧⁡𝜽 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§10.7: Introduction to Polar Coordinates Review Plot 𝟑, 𝟔𝟎° on a regular graph. 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§10.7: Introduction to Polar Coordinates Example 1 Plot 𝟑, 𝟔𝟎° on a polar graph. 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§10.7: Introduction to Polar Coordinates Example 2 Plot 𝟑, − 𝟓𝝅 𝟔 on a polar graph. 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§10.7: Introduction to Polar Coordinates Example 3 Plot −𝟑, − 𝝅 𝟔 on a polar graph. 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§10.7: Introduction to Polar Coordinates Your Turn Plot A −𝟐, 𝟓𝝅 𝟒 and B −𝟏, − 𝟑𝝅 𝟒 on a polar graph. 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

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° 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§10.7: Introduction to Polar Coordinates Recall Plot 𝟑, 𝟔𝟎° on a polar graph. Are there other ways of labeling this point? 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§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 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§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 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§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 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates

§10.7: Introduction to Polar Coordinates Assignment Worksheet 2/22/2019 9:50 AM §10.7: Introduction to Polar Coordinates