Problem 1E: Plot the points with polar coordinates (2,6) and (3,2). Give two alternative sets of coordinate... Problem 2E Problem 3E Problem 4E Problem 5E: What is the polar equation of the vertical line x = 5? Problem 6E: What is the polar equation of the horizontal line y = 5? Problem 7E Problem 8E Problem 9E: Graph the points with the following polar coordinates. Give two alternative representations of the... Problem 10E: Graph the points with the following polar coordinates. Give two alternative representations of the... Problem 11E Problem 12E Problem 13E Problem 14E: Points in polar coordinates Give two sets of polar coordinates for each of the points AF in the... Problem 15E: Converting coordinates Express the following polar coordinates in Cartesian coordinates. 15. (3,4) Problem 16E: Converting coordinates Express the following polar coordinates in Cartesian coordinates. 16. (1,23) Problem 17E: Converting coordinates Express the following polar coordinates in Cartesian coordinates. 17. (1,3) Problem 18E: Converting coordinates Express the following polar coordinates in Cartesian coordinates. 18. (2,74) Problem 19E: Converting coordinates Express the following polar coordinates in Cartesian coordinates. 19. (4,34) Problem 20E: Converting coordinates Express the following polar coordinates in Cartesian coordinates. 20. (4, 5) Problem 21E: Converting coordinates Express the following Cartesian coordinates in polar coordinates in at least... Problem 22E: Converting coordinates Express the following Cartesian coordinates in polar coordinates in at least... Problem 23E: Converting coordinates Express the following Cartesian coordinates in polar coordinates in at least... Problem 24E: Converting coordinates Express the following Cartesian coordinates in polar coordinates in at least... Problem 25E: Converting coordinates Express the following Cartesian coordinates in polar coordinates in at least... Problem 26E: Converting coordinates Express the following Cartesian coordinates in polar coordinates in at least... Problem 27E Problem 28E Problem 29E Problem 30E Problem 31E Problem 32E Problem 33E Problem 34E Problem 35E Problem 36E Problem 37E Problem 38E Problem 39E Problem 40E Problem 41E: Graphing polar curves Graph the following equations. Use a graphing utility to check your work and... Problem 42E: Graphing polar curves Graph the following equations. Use a graphing utility to check your work and... Problem 43E Problem 44E Problem 45E: Graphing polar curves Graph the following equations. Use a graphing utility to check your work and... Problem 46E: Graphing polar curves Graph the following equations. Use a graphing utility to check your work and... Problem 47E: Graphing polar curves Graph the following equations. Use a graphing utility to check your work and... Problem 48E: Graphing polar curves Graph the following equations. Use a graphing utility to check your work and... Problem 49E Problem 50E Problem 51E Problem 52E Problem 53E: Using a graphing utility Use a graphing utility to graph the following equations. In each case, give... Problem 54E: Using a graphing utility Use a graphing utility to graph the following equations. In each case, give... Problem 55E Problem 56E: Using a graphing utility Use a graphing utility to graph the following equations. In each case, give... Problem 57E: Using a graphing utility Use a graphing utility to graph the following equations. In each case, give... Problem 58E: Using a graphing utility Use a graphing utility to graph the following equations. In each case, give... Problem 59E Problem 60E Problem 61E Problem 62E: Cartesian-to-polar coordinates Convert the following equations to polar coordinates. 62. y = 3 Problem 63E: Cartesian-to-polar coordinates Convert the following equations to polar coordinates. 63. y = x2 Problem 64E: Cartesian-to-polar coordinates Convert the following equations to polar coordinates. 64. (x l)2 +... Problem 65E: Cartesian-to-polar coordinates Convert the following equations to polar coordinates. 65. y = 1/x Problem 66E Problem 67E Problem 68E Problem 69E Problem 70E Problem 71E Problem 72E Problem 73E Problem 74E Problem 75E: Circles in general Show that the polar equation r22rr0cos(0)=R2r02 describes a circle of radius R... Problem 76E Problem 77E Problem 78E Problem 79E Problem 80E Problem 81E Problem 82E: Equations of circles Find equations of the circles in the figure. Determine whether the combined... Problem 83E Problem 84E Problem 85E Problem 86E Problem 87E Problem 88E Problem 89E Problem 90E: Limiting limaon Consider the family of limaons r = 1 + b cos . Describe how the curves change as b ... Problem 91E Problem 92E Problem 93E Problem 94E: The lemniscate family Equations of the form r2 = a sin 2 and r2 = a cos 2 describe lemniscates (see... Problem 95E: The rose family Equations of the form r = a sin m or r = a cos m. where a is a real number and m is... Problem 96E Problem 97E Problem 98E: The rose family Equations of the form r = a sin m or r = a cos m. where a is a real number and m is... Problem 99E Problem 100E Problem 101E Problem 102E: Spirals Graph the following spirals. Indicate the direction in which the spiral is generated as ... Problem 103E Problem 104E Problem 105E Problem 106E Problem 107E: Enhanced butterfly curve The butterfly curve of Example 8 is enhanced by adding a term:... Problem 108E Problem 109E Problem 110E Problem 111E Problem 112E: Cartesian lemniscate Find the equation in Cartesian coordinates of the lemniscate r2 = a2 cos 2,... Problem 113E Problem 114E format_list_bulleted