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1. y=sin(x), x can be _____, but without units is always _____.
radians or degrees, radians

2. pi radians is ____ degrees
180

The unit of sin(x) is
none

____is unitless because it is defined as arc length/radius
radian

y=A*sin(x), A is
amplitude

y=A*sin(w*t), t is _____ and w is _____.
time in seconds, frequency in radians/second

y=A*sin(w*t), w is
2*pi*f

y=A*sin(2*pi*f*t), f is frequency
cycles/second or Hertz

y=A*sin( t * 2 * pi / T ), T is ______ measured in ______.
cycles/second or Hertz

y=A*sin(2*pi*f*t), f is
1/T

y=A*sin(w*t + theta), theta is _____, measured in ______.
phase shift (or angle), degrees or radians

y=A*sin(w*t + theta) + B, B is _____ shift, measured with same unit as ______.
vertical, A

cos(x) = sin(x _____)
+pi/2

sin(x) = cos(x _____)
pi/2

Time of 123 ms is _____ seconds
0.123

Time of 123456 us is _____ seconds
0.123456

Any angle given without units is ALWAYS
radians

If an angle has units of degrees, then the degree unit ____ be written, because radians will be assumed otherwise.
must

The derivative of a contant is
not defined

The derivative of a function that has a constant value is
another function whose constant value is zero

Derivative operator is a _______ operator
slope

All of the following are equivalent. The best way to verbalize _____ is derivative of y with respect to x.
dy(x)/dx

All of the following are equivalent. The best way to verbalize _____ is derivative with respect to x of y
(d/dx)y(x)

All of the following are equivalent. The best way to verbalize _____ is yprime of x.
y'(x)

The best way to verbalize _____ is yprime.
y'

y' and y'(x) and (d/dx)y(x) and dy(x)/dx and dy/dx all mean the same thing
true

The value of y at x=x1 is
4 answers
 y(x1)
 y'(x1)
 dy/dx  x=x1
 (d/dx)y(x)  x=x1

The independent variable in y(x) is
x

The dependent variable in y(x) is
y

h'(x) = g(x) and h(x)=x^n. g(x)=
n*x^(n1)

h'(x) = g(x) and h(x)=sin(x), g(x)=
cos(x)

h'(x) = g(x) and h(x)=cos(x), g(x)=
sin(x)

e=2.718 and e^1 and exp(1) all mean the same thing
true

h'(x) = g(x) and h(x)=exp(x), g(x)=
h'(x) + g'(x)

(d/dx)( a*h(x) + b*g(x) ) =
a*h'(x) + b*g'(x)

(d/dx)( h(x) / g(x) ) =
(h'*g  h*g') / g^2

y(x) = M*x + B. The slope of the line normal to y(x) is
1/M

The square root of 1 is
the symbol i (usually and in calculators) or the symbol j (in electrical engineering)




A complex number is
like a 2D vector

Complex numbers
are frequently used in electrical engineering

The number (3+i4) is an example of a _______ number in rectangular form.
complex

The real part of 3+i4 is
3

The imaginary part of 3+4i is
4

The magnitude of 3+i4 is
5

The angle of 3+i4 is
53.13 DEG

The sum of 3 and 4i is
3+4i

The magnitude of the sum of 3 and i4 is
5

The angle (radians) of the sum of 3 and i4 is
0.9273

exp(1)=e^(1) is known as Euler's number and is
2.71828

exp(i*pi)*1=e^(i*pi)*1 is a complex number in polar form and is the same as
1

exp(i*pi)*2=e^(i*pi)*2 is a complex number in polar form and is also
2

exp(i*pi/2)*3=e^(i*pi/2)*3 is a complex number in polar form and is also
3i

The sum of 3 and 4i is
 exp(0.927i)*5
 5*exp(0.927i)
 both of these

The sum of 3 and i4 has an angle of
 both of these
 53.13 degrees
 0.927 radians

Complex numbers can be
 all of these
 multiplied and divided
 added and subtracted
 raised to powers
 placed in matrices

exp(i*z) is the same as
cos(z)+i*sin(z), which is know as Euler's formula

sin(z), cos(z), tan(z), ln(z), log(z) are defined when z is a complex number
TRUE

AC voltage of 5*exp(i53.13 deg) has an amplitude of
5 volts

AC voltage of 5*exp(0.927i) has an phase of
0.927 radians

Euler's identity (e^(i*pi)+1=0) contains all the special numbers: 0, 1, e, i, and pi, and has been called the most profound equation in all of mathematics.
true

Some say that Euler's identity (e^(i*pi)+1=0) is so mysterious that it can hardly be comprehended.
true

Engineering technology students know that Euler's identity (e^(i*pi)+1=0) is easy to understand, because e^(i*pi) is a complex number in polar form and is equal to 1.
true

A vector that has a length of one is called a ______ vector.
unit

vector = [1.2, 3.4, 5.6], where 1.2 is called the _____ component
first

The dot product of two 3D vectors is

a scalar (not a vector), which is the same as a number

The dot product is useful for calculating the angle between two vectors:
(2D or 3D)

The dot product of two vectors A and B is defined as dotP(A,B)=
norm(A) * norm(B) * cos(theta)

The length of a 3D vector A=[a,b,c] is norm(A)=
sqrt(a*a + b*b + c*c)

The magnitude of the cross product of two vectors A and B is
norm(A)*norm(B)*sin(theta)

The cross product of two 3D vectors is
a 3D vector

The cross product of two 3D vectors is useful
in 3D torque problems

A 3D vector with components a,b, and c can be stored into a row vector as
[a,b,c]

A 3D vector with components a,b, and c can stored into a column vector as
[a;b;c]

The dotproduct operation is commutative which means dotP(a,b) = dotP(b,a)
true

The crossproduct operation is commutative which means crossP(a,b) = crossP(b,a)
false

Regarding a,b,c in crossP(a,b) = c,
all are 3D vectors

In crossP(a,b) = c
c is perpendicular to both a and b

acos( dotP(a,b) / ( norm(a) * norm(b) ) ) sto> nn(a,b) is a TI89 function that computes the
angle between vectors a and b

The formula for calculating torque is
R cross F = crossP(R,F)

In calculating torque about pointO by crossP(R,F), R
a vector from pointO to any point on the line of action of forceF

In calculating torqueT about pointO by T=crossP(R,F), the direction of T
perpendicular to both R and F and is given by the righthand rule

x/norm(x) sto> uu(x) is a TI89 function. Then typing: uu(A) will calculate the ______ of vectorA
unit vector in the direction

The augment function in the TI89
combines two vectors into a matrix

ginverse multiplied by the weight vector in Video H300475 at 2:19 is an error, because [0;0;100]
is the negative of the weight vector

The number of radians in 180 degrees is
pi

The number of degrees in one radian is approximately
57

The angle measured in radians is

the arc length divided by the radius

The dimension of a radian is
dimensionless

The number of gradians in 360 degrees is
400

Angles are measured relative to the
positive x axis

Positive angles "go" _______ from the ________.
counterclockwise, xaxis

A vector with an angle of pi/2 radians point along the _____ axis
+y

A vector with an angle of pi radians point along the _____ axis
x

A vector with an angle of negativepi radians point along the _____ axis
x

A vector with an angle of negativepi/2 radians point along the _____ axis
y

The maximum airplane angle is _____ degrees
90

Airplane angles are measured from
North or South

An airplane angle of ____ is the same as 100 degrees.


Airplane angles are
always positive

TI89 angles are measured
positive when counterclockwise from xaxis

The matrix method in solving simulaneously linear equations is most efficient because
the unknown variables, x and y, are not entered into the calculator

ToB=torque in Newtonmeters (Nm) about pointo due to forceB is
24

ToA=torque in Newtonmeters (Nm) about pointo due to forceA is
0

ToB dirction is
counterclockwise

ToB vectordirction is perpendicular to the figure and is directed
out

Torque (Nm) about pointo due to forceA and forceB simultaneously is
24

Torque direction about pointo due to forceA and forceB simultaneously is
counterclockwise

Torque vector direction about pointo due to forceA and forceB simultaneously is
out

ForceA + ForceB is equal to ForceC
true

ForceC can be replaced by forceA and forceB
true

ForceC can be resolved into forceA and forceB.
true

The two components of forceC are forceA and forceB.
true

ToC=torque in Newtonmeters (Nm) about pointo due to forceC is
24

ToC direction is
counterclockwise

ToC vectordirction is perpendicular to the figure and is directed
out

The angle measured in radians is
the arc length divided by the radius

An angle of one radian occurs when the ____ and the arc length are ___
radius, the same

Torque about the nut axis in Fig. 1
is force multiplied by distance that is perpendicular to the force

The nut axis in Fig. 1
perpendicular to the page

The torque direction in Fig. 1 is
counterclockwise

The vectortorque direction in Fig. 1 according to the righthand rule is
perpendicular to the page (nut axis) pointing out

The torque applied to the lug nut in Fig. 2 is
downward force multiplied by the distance from his hand to the nut axis

The purpose for the wrench extention in Fig. 3 is
both of these

The purpose for the wrench extra extention in Fig. 4 is
both of these

The removal of the trucklug nut as demonstrated is possible if the nut is
left handed

At 2:10, the number of equations in the green box is
2

At 2:10, the equations in the green box are linear because
 the graph of y(x) is linear
 x and y are raised to the first power

At 2:10, the slope of 4x+5y=23 is
4/5

At 2:10, the slope of 6x7y=9 is
6/7

At 2:10, the yaxis intercept of 4x+5y=23 is
23/5

At 2:10, the yaxis intercept of 6x7y=9 is
9/7

At 2:10, the number of equations in the blue box is
1

At 2:10, the first matrix in the blue box is
twobytwo or 2x2

At 2:10, the second matrix in the blue box is
twobyone or 2x1

At 2:10, the third matrix in the blue box is
twobyone or 2x1

At 2:10, a is
a matrix with four elements

At 2:10, b is
a matrix or vector with two elements

At 2:10, c is
a matrix or vector with two elements





At 3:00, the top equation in the blue box
enters the four elements of the 2x2 a matrix

At 3:00, the middle equation in the blue box
enters the two elements of the 2x1 c matrix

At 3:00, the third equation in the blue box
solves for the variables x and y

At 3:00, the commas in the blue box separates
elements in that row

At 3:00, the semicolons in the blue box separates
rows

The matrix method in solving simulaneously linear equations is most efficient because
the unknown variables, x and y, are not entered into the calculator















