Vectors
Parametrics
Polar
Complex
Random
100
100
100
100
100
200
200
200
200
200
300
300
300
300
300
400
400
400
400
400
500
500
500
500
500
Find the unit vector in the direction
of < -4, -5 >
−4 −5
,
41 41
€
Find the magnitude and direction
angle of 3i – 4j
Magnitude: 5
Angle: 53.13º
Find the angle between the two
vectors:
< 2, 3 > and < -2, 5 >
55.5º
The vector describing a planes direction
and speed is < 30, -40 >.
Find its bearing & speed.
Bearing: 143ishº
Speed: 50mph
An airplane is flying on a bearing of
340º at 325mph.
Wind is blowing with the bearing of
320º and 40mph.
Find the actual bearing of the plane.
337.84º
Eliminate the parameter:
x=1+t
y=t
Have your answer be “y = something”
y=x-1
Eliminate the parameter:
x = 2t – 3
y = 9 – 4t
Have your answer be
“y = something”
y = -2x + 3
Eliminate the Parameter
x = t2
y=t+1
Have your answer be
“x = something”
x = y2 - 2y + 1
Eliminate the Parameter
x = 5 cos t
y = 5 sin t
AND identify the curve
x2 + y2 = 25
Circle with radius 5
Eliminate the Parameter
y = e5t
x = e20t
make your answer “y=something”
y = x1/4
Convert from polar to
rectangular coordinates:
(3,
5π
6
)
(have your answer
in decimal form)
€
(-2.6, 1.5)
Convert from rectangular
to polar coordinates:
(-1, 1)
(leave in radical/radian form)
3π
( 2, )
4
€
or
π
(− 2,− )
4
Convert from polar to rectangular
form: r = 4 sec (theta)
AND describe the graph
x=4
a line...
Convert from rectangular to polar
form: (x – 3)2 + (y – 2)2 = 13
r = 6 cos (theta) + 4 sin (theta)
Name these three graphs and state
their maximum r values:
1. r = 3 cos 2(theta)
2. r = 2 + 2 cos(theta)
5
r=
3.
cosθ + 2sin θ
€
1. Rose curve -max r = petal length 3 (4 petals)
2. Limacon – Cardiod
max r = 4
3. Line x + 2y = 5
(no max r)
A = 5[cos(50) + i sin(50)]
B = 4[cos(40) + i sin(40)]
Find the length, angle, and a + bi
form of A*B.
Length: 20
Angle: 90º
20i
Find [3(cos45º + isin45º)]4
in a + bi form.
81(cos(180) + i sin(180))
becomes...
-81
Find (3 + i)10
in a + bi form.
-99712 – 7584i
Yikes!
Find the cube roots−4
of + 4i 3
in trigonometric form
€
2(cos(40º) + isin(40º))
2(cos(160º) + isin(160º))
2(cos(280º) + isin(280º))
Find the other points of a square
centered on the origin with one
corner 5on + 3i
34
€
34
−3
5i
+
34
34
5
3i
+
34
34
€
−5
−3i €
+
34
34
3
−5i
+
34
34
€
€
Who is Mrs. Allen’s favorite
Disney Princess?
Ariel/The Little Mermaid
Where did Mrs. Allen go to
college?
CSULB
If you add up
1 + 2 + 3 + 4 +.... + 99 + 100
what do you get?
5050
How can you add eight 8’s to
make 1000? (Addition only)
888 + 88 + 8 + 8 + 8 = 1000
What is the derivative of
x2 + 3x - 1
2x + 3