YORK UNIVERSITY YORK UNIVERSITY
Department of Mathematics and Statistics
MATH 1025 W

Assignment 1: Polar Coordinates and Complex Numbers

  1. Find polar coordinates of the points whose Cartesian coordinates are:
    (a)
    (2,2);
    (b)
    (3,-1);
    (c)
    (0,2);
    (d)
    (-3,-6);
    (e)
    (2,-2);
    (f)
    (-3,3).
  2. Find the Cartesian coordinates of the points whose polar coordinates are:
    (a)
    (1,[(p)/4]);
    (b)
    (2,-[(p)/4]);
    (c)
    (2,-[(5p)/6]);
    (d)
    (-2,[(7p)/6]).
  3. Identify and sketch the graphs of the following curves:
    (a)
    r = 2sin2q;
    (b)
    r = 2q;
    (c)
    r = sinq+ cosq.
  4. Find all points of intersection of the curves r = sinq and r2 = 3cos2 q.
  5. Convert the following Cartesian coordinates in 3-dimentions into cylindrical polar form:
    (a)
    (2,2,3);
    (b)
    (43,-4,6);
    (c)
    (3,1,-2).
  6. Convert the following cylindrical polar coordinates in 3-dimentions into Cartesian form:
    (a)
    (6,[(p)/6],2);
    (b)
    (4,[(4p)/3],-8).
  7. Describe the following curves or surfaces given in cylindrical polar coordinates:
    (a)
    q = [(p)/6], r = -2;
    (b)
    r = cosq;
    (c)
    z = 2r;
    (d)
    r = 4, z = q.
  8. Convert the following Cartesian coordinates in 3-dimentions into spherical coordinates:
    (a)
    (2,-23,4);
    (b)
    (-2,2,23).
  9. Convert the following spherical polar coordinates into Cartesian form:
    (a)
    (8,[(p)/4],[(p)/6]);
    (b)
    (4,[(p)/3],[(3p)/4]).
  10. Describe the following curves or surfaces given in spherical polar coordinates:
    (a)
    f = [(p)/6];
    (b)
    r = 5, f = [(p)/3];
    (c)
    r = 3cosf;
    (d)
    rsinf = cosf.

Anton and Rorres

  1. Section 10.1
    Question 4 (b), (d), (e), (f)
    Question 9 (b), (c)
    Question 10 (c), (d).
  2. Section 10.2
    Question 1 (c),(e)
    Question 2 (d), (e)
    Question 8.
  3. Section 10.3
    Question 3 (c), (d), (e)
    Question 5
    Question 10.

The end




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On 6 Mar 2001, 16:34.