MATH 1172 Midterm: MATH 1172 Ohio State University Math 1172 11.2 Solutions Fa 2014

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

November 5, 2015: graph the following its in polar coordinates: Solution: multiplying through by r we have (3, /4) (1, 5 /6) ( 2, /2) ( 3, 7 /4) r2 = 6r cos( ) Since r2 = x2 + y2 and x = r cos( ), we have x2 + y2 = 6x. This is an appropriate representation of the function in cartesian coordinates, but we can simplify things through a bit of algebra x2. 6x + 9 + y2 = 9 (x 3)2 + y2 = 32: graph the curve r = 2 2 sin( ). Solution: let us calculate some values of the curve at speci c values of . a at = 0: (1, 2 /3) is a pt in polar coor- dinates. Solution: x = 1 cos(2 /3) = 1. 2 y = 1 sin(2 /3) : (2, 2) is a pt in cartesian coordinates. Solution: r = p22 + 22 = 2 2.