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)
(Ö3,-1);
(c)
(0,2);
(d)
(-3,-6);
(e)
(Ö2,-Ö2);
(f)
(-3,Ö3).
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)
(4Ö3,-4,6);
(c)
(Ö3,1,-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,-2Ö3,4);
(b)
(-Ö2,Ö2,2Ö3).
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.