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# MAT 110 Chapter 10 Study Guide MAT 110

Barry University

GPA 3.7

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This 5 page Study Guide was uploaded by Sterling on Wednesday September 14, 2016. The Study Guide belongs to MAT 110 at Barry University taught by Dr. Singh in Fall 2016. Since its upload, it has received 5 views. For similar materials see Precalculus Mathematics 2 in Mathmatics at Barry University.

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Date Created: 09/14/16

MAT 110 Precalculus Mathematics 2 Chapter 10 Study Guide Notes L. Sterling September 28th, 2016 Abstract Provide a generalization to each of the key terms listed in this section. 1 Polar to Rectangular Coordinates Rectangular Coordinates = Cartesian Coordinates P : Point Polar Coordinates : (r; ▯) Rectangular Coordinates : (x; y) x = r cos ▯ y = r sin ▯ 1 2 Rectangular to Polar p r = x + y2 r = x + y 2 y tan ▯ = [x 6= 0] x 3 Polar to Rectangular Multiply both sides by "r": Square both sides: 4 Rectangular Coordinates (r; ▯) 5 Polar Coordinates (x; y) 6 Theorem: Horizontal and Vertical Line 6.1 Horizontal Line a : Real Number Equation : r sin ▯ = a a ▯ 0 : a units lying above the pole a < 0 : jaj units below the pole 2 6.2 Vertical Line Equation : r cos ▯ = a a ▯ 0 : Units lying to the right of the pole a < 0 : jaj units to the left of the pole 7 Theorem: Horizontal and Vertical Line 7.1 Horizontal Line a : Real Number Equation : r sin ▯ = a a ▯ 0 : a units lying above the pole a < 0 : jaj units below the pole 7.2 Vertical Line Equation : r cos ▯ = a a ▯ 0 : Units lying to the right of the pole a < 0 : jaj units to the left of the pole 8 Theorem: Equations and Circles Descriptions 8.1 r = 2a sin ▯ Radius : a Center : (0; a) 3 8.2 r = ▯2a sin ▯ Radius : a Center : (0; ▯a) 8.3 r = 2a cos ▯ Radius : a Center : (a; 0) 8.4 r = ▯2a cos ▯ Radius : a Center : (▯a; 0) 8.5 Circles Every circle would be passing through the pole: 9 Theorem: Symmetry Tests [in terms of in po- lar equations] 9.1 Symmetric, but with respect to the Polar Axis: X- Axis Replace ▯ ! ▯▯ 4 9.2 Symmetric, but with respect to the Line: Y ▯ Axis [▯ = ] 2 Replace ▯ ! ▯ ▯ ▯ 9.3 Symmetric, but with respect to the Pole: Origin Replace r ! ▯r 10 Cardioids 10.1 Formed Equations [When a > 0] r = a(1 + cos ▯) r = a(1 + sin ▯) r = a(1 ▯ cos ▯) r = a(1 ▯ sin ▯) 10.2 Graph Passes through the Pole h i a Alternative Form when b = 2 ! 2b = a : r = 2b(1 + cos ▯) r = 2b(1 + sin ▯) r = 2b(1 ▯ cos ▯) r = 2b(1 + sin ▯) 5

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