#$&*
course mth 164
1:10 pm on July 9
Some problems form 9.1(match each point in polar coordinates with either A,B, C or D on the graph)
11. (2, -11 pi/6)= A
12. (-2, - pi/6)= C
15. (2, 5pi/6)= B
18. (2, 11 pi/6)= D
Plot in polar coordinates
19. ( 3, 90 degrees)
I drew a 90 degree angle, and on the y axis part, I counted 3 spaces up and placed a mark. I labeled in (3, 90 deg.)
21. (-2,0)
I drew a straight line along the x axis and labeled the point 0. I then labeled the point (-2,0).
27. (-1, -pi/3)
For this one I drew the angle that pi/3 makes, both above and below the x axis. I labeled the mark 1 on the pi/3.
@& That mark would go on the part of your line that goes below the x axis.*@
30. (-3, - pi/2)
I drew a 90 degree angled (negative because of - pi/2) and counted 3 spaces down to -3 and labeled the points (-3, -pi/2).
31. (5, 2pi/3)
I drew the angle 2 pi/3 and counted up 5 places and made a mark. I labeled it (5, 2 pi/3).
a. (5, -4 pi/3)
b. (-5, 5 pi/3)
c. (5, 8 pi/3)
33. (-2, 3 pi)
I drew a straight line along the x axis and labeled the point 0. I marked the spot (-2, 3 pi) and labeled it.
a. (2, -2 pi)
b. (-2, pi)
c. (2, 2 pi)
39. (3, pi/2) Find the rectangular coordinates
x- r cos theta
y= r sin theta
r= 3, theta= pi/2
x= r cos theta= 3 cos pi/2
y= r sin theta= 3 sin pi/2
= (0, 3)
45. (-2, 3 pi/4)
R= -2, theta= 3 pi/4
X= r cos theta
Y= r sin theta
X= -2 cos 3 pi/4
Y= -2 sin 3 pi/4
= (sqrt 2, sqrt 2)
51. (7.5, 110 degrees)
X= r cos theta
Y= r sin theta
R= 7.5, theta= 110 degrees
X= 7.5 cos 110
Y= 7.5 sin 110
= (-2.57, 7.05)
55. (3, 0)
R= sqrt x^2 + y^2= 3^2 + 0^2= sqrt 9= 3
Tan theta= y/x
Theta= tan^-1 (y/x)= tan^-1 (0/3)
Tan^-1(-1)= theta
= (3, 0)
59. (1, -1)
R= sqrt x^2 + y^2= sqrt 1^2 + (-1^2)= sqrt 2
Tan theta= y/x
Theta= tan^-1 (y/x)
Tan^-1 (-1/1) = - pi/4
( sqrt 2, - pi/4)
69. x^2= 4y
X= r^2 cos 41
X= r cos theta
Y= r sin cos theta
= r^2 cos^2 theta - 4r sin theta = 0
75. r= cos theta
X= r cos theta
Y= cos theta
= x^2 + y^2 - x= 0
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&#Your work looks good. See my notes. Let me know if you have any questions. &#