Pre-Cal D Semester Quiz Terms

Front 1

the measure formed by two rays having a common endpoint

Back 1

angle

Front 2

an angle whose vertex is located at the origin and whose initial side falls on the positive x-axis

Back 2

standard position

Front 3

90 deg
180 deg
270 deg
360 deg

Back 3

1st, 2nd, 3rd, 4th quadrant angle

Front 4

an angle in standard position where the terminal side falls on an axis

Back 4

quadrantal angle

Front 5

an angle whose vertex is at the center of the circle

Back 5

central angle

Front 6

measure of a central angle whose initial arc is equal to the measure of the circle's radius

Back 6

radian

Front 7

s=r(theta), theta in radians

Back 7

arc length formula

Front 8

angle swept out in one unit of time by segment from center of circle to point on circumference

Back 8

angular speed

Front 9

distance traveled in one unit of time by a point on the circumference of circle

Back 9

linear speed

Front 10

sector area

Back 10

As=1/2(theta)r^2, theta in radians

Front 11

right triangle difs of trig functions

Back 11

sin(theta)=opp/hyp csc(theta)=hyp/opp
cos(theta)=adj/hyp sec(theta)=hyp/adj
tan(theta)=opp/adj cot(theta)=adj/opp

Front 12

an equation which is true for all allowable values of the variable

Back 12

identity

Front 13

coordinate system defs of trig functions

Back 13

sin(theta)=y/r csc(theta)=r/y
cos(theta)=x/r sec(theta)=r/x
tan(theta)=y/x cot(theta)=x/y

Front 14

two angles in standard position who have the same terminal side

Back 14

coterminal angles

Front 15

an acute angle formed by the terminal side of the given angle and the x-axis

Back 15

reference angle

Front 16

a circle whose radius is one and whose center is at the origin of a rectangular coordinate system

Back 16

unit circle

Front 17

unit circle defs of trig functions

Back 17

sin(t)=b
cos(t)=a
tan(t)=b/a
csc(t)=1/b
sec(t)=1/a
cot(t)=a/b

Front 18

F(theta+p)=f(theta)

Back 18

periodic function

Front 19

period

Back 19

2pi/w

Front 20

cos(-theta)=cos(theta) sec(-theta)=sec(theta)

Back 20

even function

Front 21

sin(-theta)=-sin(theta) csc(-theta)=-csc(theta)
tan(-theta)=-tan(theta) cot(-theta)=-cot(theta)

Back 21

odd function

Front 22

amplitude

Back 22

absolute value of A if y=Asinx

Front 23

an equation which is true for only some allowable values of the variable

Back 23

conditional equation

Front 24

identities (33)

Back 24

quotient(2), reciprocal(3), pythagorean(3), even/odd(6), cos/sin/tan sum&difference formulas(6), double angle/half angle(8), right triangle defs(6)

Front 25

principal values for inverse trig functions

Back 25

arcsine −π/2 ≤ y ≤ π/2
arccosine 0 ≤ y ≤ π
arctangent −π/2 < y < π/2
arccotangent 0 < y < π
arcsecant 0 ≤ y < π/2 or π/2 < y ≤ π
arccosecant −π/2 ≤ y < 0 or 0 < y ≤ π/2

Front 26

an acute angle formed by the line of sight looking up at an object and the horizontal

Back 26

angle of elevation

Front 27

an acute angle formed by the line of sight looking down at an object and the horizontal

Back 27

angle of depression

Front 28

a triangle where none of the angles measure 90 degrees

Back 28

oblique triangle

Front 29

Sin Law

Back 29

a/sin(alpha) = b/sin(beta) = c/sin(gamma)

Front 30

Cosin Law

Back 30

a^2=b^2+c^2-2bccos(alpha)

Front 31

triangle area formulas (4)

Back 31

K=1/2(base)(height)
K=1/2absin(gamma)
K=the square root of s(s-a)(s-b)(s-c)
K=(a^2)/2 x [sin(beta)sin(gamma)]/sin(alpha)

Front 32

any number of the form a+bi where a&b are real numbers and i is equal to the square root of negative one

Back 32

complex number

Front 33

complex number a+bi where b does not equal zero

Back 33

imaginary number

Front 34

complex number a+bi where b does not equal zero and a does equal zero

Back 34

pure imaginary number

Front 35

absolute value of complex number

Back 35

square root of a^2+b^2

Front 36

theorem for multiplying complex numbers

Back 36

z1z2=rs[cos(alpha+beta)+isin(alpha+beta)]

Front 37

theorem for dividing complex numbers

Back 37

z1/z2=r/s[cos(alpha-beta)+isin(alpha-beta)]

Front 38

DeMoivre's theorem for powers/roots

Back 38

z^n=r^n[cos(ntheta)+isin(ntheta)]

Front 39

polar equations

Back 39

contain r and/or theta

Front 40

theta=#

Back 40

line through pole

Front 41

r=#

Back 41

circle w/ center at the pole

Front 42

r=#sin(theta)

Back 42

circle through pole

Front 43

rsin(theta)=#

Back 43

horizontal line

Front 44

rcos(theta)=#

Back 44

vertical line

Front 45

r=m+ncos(theta) or r=m+nsin(theta) where the absolute value of n is equivalent to the absolute value of m

Back 45

cardioid

Front 46

r=m+ncos(theta) or r=m+nsin(theta) where the absolute value of n is greater than the absolute value of m

Back 46

limacon w/loop

Front 47

r=m+ncos(theta) or r=m+nsin(theta) where the absolute value of m is greater than the absolute value of n

Back 47

limacon w/o loop

Front 48

r=cos(#theta) or r=sin(#theta)

Back 48

rose

Front 49

r^2=ncos(#theta)

Back 49

lemniscate

Front 50

a quantity that has both magnitude and direction

Back 50

vector

Front 51

two vectors with the same magnitude and direction

Back 51

equal vectors

Front 52

negative of vector

Back 52

vector+(-vector)=0

Front 53

zero vector

Back 53

vector + zero=zero + vector=vector

Front 54

subtraction of vectors

Back 54

<a-c, b-d>

Front 55

a vector for which the magnitude is one

Back 55

unit vector

Front 56

an algebraic vector whose initial point is at the origin

Back 56

position vector

Front 57

vector i
vector j

Back 57

i=<1,0>
j=<0,1>

Front 58

a quantity with only magnitude

Back 58

scalar

Front 59

they are
1.nonzero scalar multiples of each other
2.the same or opposite direction

Back 59

parallel vectors

Front 60

two nonzero vectors where the angle between is pi/2

Back 60

orthogonal (perpendicular) vectors

Front 61

magnitude of a vector

Back 61

the square root of a^2+b^2

Front 62

direction of a vector

Back 62

tan(theta)=b/a
=>consider quadrant

Front 63

unit vector in the direction of a vector

Back 63

u=v/absolute value of v

Front 64

component form for a vector

Back 64

<a,b>

Front 65

polar form for a vector

Back 65

(r, theta)

Front 66

vector written in terms of unit vectors

Back 66

v=ai+bj

Front 67

dot product

Back 67

v dot w=ac+bd

Front 68

angle between vectors

Back 68

cos(theta)=(v dot w)/lvllwl

Front 69

projection of v onto w

Back 69

v1=[(v dot w)/lwl^2]w

Front 70

properties of dot product (4)

Back 70

1. communative
2. distributive
3. v dot v=lvl^2
4. 0 dot v=0

Front 71

vectors can be added geometrically by two methods...

Back 71

1. parallelogram
2. consecutive method

Front 72

Two vectors are orthogonal iff

Back 72

their dot product is zero