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April 17, 2012 9.6 Polar Coordinates - Day 1 Plotting Points April 17, 2012 Multiple representations of the same point in polar coordinates. April 17, 2012 Converting between Polar and Rectangular Coordinates Polar and rectangular coordinates are related in the triangle above as: tan θ = y/x sin θ = y/r cos θ = x/r Use the following relationships to convert from rectangular coordinates to polar coordinates: x = r cos θ y = r sin θ Use the following relationships to convert from polar coordinates to rectangular coordinates: tan θ = y / x r 2 = x2 + y2 Plot the point (5, 120º) and convert to rectangular coordinates. Plot the point (-1/2, √3/2) and convert to polar coordinates. April 17, 2012 More practice with converting between polar and rectangular coordinates. Use the following relationships to convert from rectangular coordinates to polar coordinates: x = r cos θ y = r sin θ Use the following relationships to convert from polar coordinates to rectangular coordinates: tan θ = y / x r 2 = x2 + y2 Convert to rectangular coordinates. Convert to polar coordinates. 1. 1. (-1, 1) 2. 2. (0, 2) April 17, 2012 Polar Coordinates - Day 2 Equation Conversion Converting an equation from Rectangular to Polar is pretty simple. Just make the substitution: x = r cos θ and y = r sin θ Convert the equations: 1. y = x 2. 4x + 7y - 2 = 0 3. 2xy = 1 4. x2 + y2 - 8y = 0 April 17, 2012 Converting an equation from Polar to Rectangular coordinates can be challenging. Use the relationships to assist you in converting the equations below. x = r cos θ y = r sin θ tan θ = y / x r2 = x2 + y2 Graph the equations below and find the rectangular equation. 1. r = 2 2. θ = π/3 April 17, 2012 3. r = sec θ 4. r2 = sin 2θ 5. r = 2 / (1 + sin θ) April 17, 2012