Unit 4

Question 1

A vector is perpendicular/orthogonal if…

Answer 1

the dot product = 0

Question 2

A vector is parallel if…

Answer 2

a1/a2 = b1/b2

Question 3

What is the formula for rectangular coordinates to polar?

Answer 3

X = r * cos theta Y = r * sin theta

Question 4

Modulus, magnitude, hypotenuse, radius

Answer 4

All the same. ||V||

Question 5

What is the formula for polar coordinates to rectangular?

Answer 5

R = root(x^2+y^2) Theta = arctan (y/x)

Question 6

What is the interval when in polar coordinates?

Answer 6

between 0 and 2pi, must also be in the same quadrant.

Question 7

What are complex numbers in rectangular form?

Answer 7

a+bi

Question 8

What are complex numbers in polar form?

Answer 8

r(cos theta + i sin theta)

Question 9

What is the formula for magnitude of a vector?

Answer 9

root(a^2+b^2)

Question 10

What is the formula for a unit vector?

Answer 10

(1/||v||)*<a,b>

Question 11

When finding the nth root, what is K?

Answer 11

K is n-1

Question 12

When finding the nth root, what is N?

Answer 12

N is the root number

Question 13

What is the formula for finding the nth root?

Answer 13

Zk = ^n root(r)[cos (theta+2piK)/n + i sin (theta+2piK)/n]

Question 14

What is DeMoivre’s theorem formula?

Answer 14

(a+bi)^2 = r^n[cos (thetan)+isin (thetan)]

Question 15

What is the formula for finding the angle between two vectors?

Answer 15

arccos ([vw]/||v||||w||) = theta

Question 16

What is the formula for a vector V projected onto W?

Answer 16

ProjwV = ([vw]/||w||^2)w

Question 17

What is the formula for finding work done?

Answer 17

W = F * D

Question 18

When finding work formula, what is F?

Answer 18

F is a force vector

Question 19

What is F denoted by in a work calculation?

Answer 19

force number*(cos theta)i+forcenumber(sin theta)j

Question 20

When finding work formula, what is D?

Answer 20

D is a distance vector

Question 21

What is D denoted by in a work calculation?

Answer 21

<x2-x1,y2-y1>

Question 22

What is a parametric equation?

Answer 22

An equation that models the travel of an object or projectile

Question 23

What is the formula for X in a parametric equation?

Answer 23

X = Vo (cos theta)t + Xo

Question 24

What is the formula for Y in a parametric equation?

Answer 24

Y = -1/2 * gt^2+(VoSin theta)*t + Yo

Question 25

What does X represent in a parametric equation?

Answer 25

X is horizontal distance

Question 26

What does Y represent in a parametric equation?

Answer 26

Y is vertical position

Question 27

What is the velocity of gravity in both forms?

Answer 27

g = 32 ft/sec^2 g = 9.8 m/sec^2

Question 28

What does g represent in a parametric equation?

Answer 28

gravity

Question 29

What does Xo represent in a parametric equation?

Answer 29

Starting X position

Question 30

What does Yo represent in a parametric equation?

Answer 30

Starting Y position

Question 31

What does Vo represent in a parametric equation?

Answer 31

Starting velocity

Question 32

What does t represent in a parametric equation?

Answer 32

Time

Question 33

What does theta represent in a parametric equation?

Answer 33

Starting angle (for example, the angle at which a ball is thrown)

Question 34

What does “eliminating a parameter” refer to?

Answer 34

Removing t from the curved graph via substitution and solving.

Question 35

How do you convert degrees to radians?

Answer 35

Multiply the degree measure by pi/180

Question 36

How do you convert radians to degrees?

Answer 36

Multiply the radian by 180/pi

Question 37

How do you find arc length?

Answer 37

s = r * theta (s = arc length, r = radius of circle, theta = angle of the arc)