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Intro to Polar Coordinates Lesson 6.5A
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2 Points on a Plane Rectangular coordinate system Represent a point by two distances from the origin Horizontal dist, Vertical dist Also possible to represent different ways Consider using dist from origin, angle formed with positive x-axis r θ (x, y) (r, θ)
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3 Plot Given Polar Coordinates Locate the following
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4 Find Polar Coordinates What are the coordinates for the given points? B A C D A = B = C = D =
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5 Converting Polar to Rectangular Given polar coordinates (r, θ) Change to rectangular By trigonometry x = r cos θ y = r sin θ Try = ( ___, ___ ) θ r x y
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6 Converting Rectangular to Polar Given a point (x, y) Convert to (r, θ) By Pythagorean theorem r 2 = x 2 + y 2 By trigonometry Try this one … for (2, 1) r = ______ θ = ______ θ r x y
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7 Polar Equations States a relationship between all the points (r, θ) that satisfy the equation Exampler = 4 sin θ Resulting values θ in degrees Note: for (r, θ) It is θ (the 2 nd element that is the independent variable Note: for (r, θ) It is θ (the 2 nd element that is the independent variable
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8 Graphing Polar Equations Set Mode on TI calculator Mode, then Graph => Polar Note difference of Y= screen
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9 Graphing Polar Equations Also best to keep angles in radians Enter function in Y= screen
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10 Graphing Polar Equations Set Zoom to Standard, then Square
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11 Try These! For r = A cos B θ Try to determine what affect A and B have r = 3 sin 2θ r = 4 cos 3θ r = 2 + 5 sin 4θ Experiment with Polar Function Spreadsheet Experiment with Polar Function Spreadsheet
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12 Assignment A Lesson 6.5A Page 424 Exercises 1 – 47 odd
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Polar Coordinates Lesson 6.5B
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14 Write Polar Equation in Rectangular Form Given r = 2 sin θ Write as rectangular equation Use definitions And identities (see inside back cover) Graph the given equation for clues
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15 Write Polar Equation in Rectangular Form Given r = 2 sin θ We know Thus And
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16 Write Rectangular Equation in Polar Form Consider 2x – 3y = 6 As before, use definitions
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17 Assignment B Lesson 6.5B Page 424 Exercises 49 – 73 odd
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