sn5_1 - Math 1432 Notes – Week 5 Popper 005 1. What is...

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Unformatted text preview: Math 1432 Notes – Week 5 Popper 005 1. What is today? A. Monday B. Tuesday C. Wednesday D. Thursday E. Friday 9.3 Polar Coordinates Polar axis From the polar axis θ (when positive) forms an angle going counterclockwise. |r| represents the distance on the ray from the pole Given polar coordinates [r, θ ], if r ≥ 0 then r is on the ray θ and if r<0 r is on ray θ + π Example 1: plot π 2 1 , 3 Example 2: plot - π 6 1 , 2 If r = 0, then the point is on the pole -> [ ] θ , = for all θ Also, [ ] [ ] π θ θ n r r 2 , , + = for integer values of n and [ ] [ ] π θ θ + =- , , r r Changing from polar form to rectangular Changing from polar form to rectangular Changing from polar form to rectangular Changing from polar form to rectangular form: form: form: form: Formulas: θ θ sin cos r y r x = = Example 3: Change 3 , 2 π to rectangular form Changing from rectangular to polar form: Changing from rectangular to polar form: Changing from rectangular to polar form: Changing from rectangular to polar form: Formulas: 2 2 2 r y x = + For θ , can use formulas above or , arctan ≠ = x x y θ Example 4: Change ( ) 3 , 1- to polar form. Testing for Symmetry Testing for Symmetry Testing for Symmetry Testing for Symmetry If [ ] [ ] [ ] [ ] [ ] [ ] θ θ π θ θ π θ θ , , , , , , r r r r r r => + =>- =>- then the graph is symmetric about the origin axis y axis x-- Example 5:...
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This note was uploaded on 07/20/2010 for the course MATH 11278 taught by Professor Jeffmorgan during the Summer '10 term at University of Houston.

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sn5_1 - Math 1432 Notes – Week 5 Popper 005 1. What is...

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