(Chapter 9 starting with 8th edition)
Section 8.1 Section 8.2 Section 8.3 Section 8.4 Section 8.5
(9.1 - 9.5 starting with 8th edition)
Section 8.1 (9.1 starting with 8th edition)
Match each point in polar coordinates with either A,B,C or D on the graph.
Plot each point given in polar
coordinates.
10. (3, 180 `deg)
12. (-3,`pi/2 )
18. (2, 3`pi /4)
20. (-4, -`pi /4)
Plot each point given in the polar coordinates, and find other polar coordinates
(r, `theta) of the point for which
28.(-3, 4`pi )
Polar coordinates of a point are given. Find the rectangular coordinates of each
point.
30. (4, 3`pi /2)
36. (-3, 5`pi /3)
40. (2,-90 deg )
42. (-3.1, 182 deg )
The rectangular coordinates of a point are given. Find the polar coordinates for
each point.
48. (0, 4)
50. (-5, 5)
54. (-0.8, -2.1)
Find the exact polar coordinates.
52. (-2, -2`sqrt(3))
The letters x and y represent rectangular coordinates. Write each equation using
polar coordinates (r, `theta)
60. y^2 = 2x
62 4 x^2 y = 1
The letters r and `theta represent polar coordinates. Write each equation using
rectangular coordinates (x, y)
66. r= cos `theta + 1
70. r= 18
72. r= 3/(3-cos `theta)
Section 8.2 (9.2 starting with 8th edition)
Identify each polar
equation by transforming the equation to rectangular coordinates. Graph each
polar equation.
6. r cos`theta=1
10. r=2 cos `theta
12. r=3 cos `theta
Match each of the graphs (A) through (H) to one of the following polar
equations. The figures are the same in both 5th and 6th editions of the text.
18. `theta = `pi/4
20. r cos(`theta) = 2
24. r sin(`theta) = 2
Identify and graph each polar equation. Be sure to test for symmetry.
30. r=4-cos `theta
36. r=2+4 cos `theta
40. r=2 cos (5`theta)
42. r^2 = sin (4`theta)
48. r=-5 cos (3`theta)
Graph each polar equation.
50. r=2/(1-2 cos `theta) (hyperbola)
54. r=3/`theta (reciprocal spiral)
60. Show that the graph of the equation r cos `theta =a is a vertical line a
units to the right of the pole if a>0 and |a| units to the left of the pole if
a<0.
Section 8.3 (9.3 starting with 8th edition)
Plot each complex number in the complex plane and write it in polar form. Express the argument in degrees.
6. –2
10. 2+`sqrt( (3?))
12.`sqrt( 5+? )
Write each complex number in rectangular form.
18.4(cos (?/2)+? sin (?/2))
20.0.4(cos 200 `deg + i sin 200 `deg)
Find zw and z/w. leave your answers in polar forms.
24.z=cos 120 `deg+isin 120 `deg
30.z=1-I
w=1-`sqrt( (3i) )
Write each expression in standard form a+bi
36. [½(cos 72 `deg+isin72 `deg)]^5
40. (`sqrt( 3-i)^6
42. (1-`sqrt( (5i))^8 )
Find all the complex roots. Leave your answer in polar form with the argument in degrees.
48.The complex cube roots of –8
50.The complex fifth roots of –I
53.show that each complex nth root of a nonzero complex number w has the same magnitude.
54. Use the result of problem 53 to draw the conclusion that each complex nth roots lies on a circle with center at the origin. What is the radius of this circle?
Section 8.4 (9.4 starting with 8th edition)
Use the vectors in the figure at the right to graph each of the following vectors. The figures are the same in the 5th and 6th editions.
6. u - v
Use the figure at the right. Determine weather the given statement is true or
false.
10. K + G = F
12. G + H + E = D
18. If ||v|| = 2 then what is || -4 v ||?
The vector v has initial point P and terminal Q. write v in the form of a i +b
j, that is, find its position vector.
20.P=(0,0); Q=(2, -7)
24.P=(-1,4); Q=(6,2)
Find ||v||.
30.v = -2i + j
Find each quantity if v=3i-5j and w=-2i+3j.
36.||v +w||
Find the unit vector having the same direction as v
40.v=20j
42.v=-5i+12j
48.if p=(2,-1) and Q=(x, -2), find all numbers x such that the vector
represented by PQ has length 5.
50.Finding Airspeed After 1 hour in the air, an airplane arrives at a point 200
miles due south of its departure point. If there was a steady wind of 30 miles
per hour from the northwest during the entire flight, what was the average
airspeed of the airplane?
Section 8.5 (9.5 starting with 8th edition)
Find the dot product of v and w and the angle between v and w.
6.v=-i+`sqrt((3j)), w=-i+j
10.v = 3i - 4j, w = 4i - 3j.
12.Find b such that the angle between v=i+bj is `pi/2 w = i - j
Decompose v into two vectors v1 and v2, where v1 is parallel to w and v2 is
orthogonal to w.
18.v=i-2j,w=3i+j
20.The pilot of an air craft wishes to head directly east but is faced with a
wind speed of 55 miles per hour from the northwest. If the pilot maintains an
airspeed of 275 miles per hour, what compass heading should be maintained? What
is the actual speed of the aircraft?
24.An airplane travels 200 miles due west and then 150 miles 60 `degnorth of
west. Determine the resultant displacement.
30.Prove property(5), 0.v=0 (. denotes the dot product)
36.Let v and w denote two nonzero vectors. Show that the vectors ||w||v+||v||w
and ||w||v-||v||w are orthogonal.