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Algebra II TRIG Flashcards. As the year goes on we will add more and more flashcards to our collection. Bring your cards every TUESDAY for eliminator practice!

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Algebra ii trig flashcards

Algebra II TRIG Flashcards

As the year goes on we will add more and more flashcards to our collection.

Bring your cards every TUESDAY for eliminator practice!

Your flashcards will be collected on every test day! At the end of the quarter the grade received will be equivalent in value to a test grade. Essentially, if you lose your flashcards it will be impossible to pass the quarter.


What will my flashcards be graded on
What will my flashcards be graded on?

  • Completeness – Is every card filled out front and back completely?

  • Accuracy – This goes without saying. Any inaccuracies will be severely penalized.

  • Neatness – If your cards are battered and hard to read you will get very little out of them.

  • Order - Is your card #37 the same as my card #37?



Vertex formula axis of symmetry

Vertex Formula(Axis of Symmetry)

What is it good for?

#1



Quadratic formula

Quadratic Formula

What is it good for?

#2


Tells us the roots x intercepts

Tells us the roots

(x-intercepts).

#2


Describe the steps for completing the square
Describe the Steps for “Completing the Square”

  • How does it compare to the quadratic formula?

#3


1.) Leading Coeff = 1 (Divide if necessary)2.) Move ‘c’ over3.) Half ‘b’ and square (add to both sides)4.) Factor and Simplify left side.5.) Square root both sides (don’t forget +/-)6.) Solve for x.*Same answer as Quadratic Formula.

#3


General form for direct variation characteristics sketch
General Form for DIRECT VARIATIONCharacteristics & Sketch

#4


General form y kx characteristics y int 0 always sketch any linear passing through the origin
General Form: y = kxCharacteristics: y –int = 0 (always!)Sketch: (any linear passing through the origin)

#4


Define inverse variation
Define Inverse Variation

#5

Give a real life example


#5


State the general form of an inverse variation equation
State the General Form of an inverse variation equation. (constant

Draw an example of a typical inverse variation and name the graph.

#6


Xy k or
xy = k or . (constant

HYPERBOLA (ROTATED)

#6



#7 (constant


Functions

FUNCTIONS (constant

BLUE CARD


Define domain define range
Define Domain (constantDefine Range

#8


#8



Vertical line test
Vertical Line Test or not?

  • Each member of the DOMAIN is paired with one and only one member of the RANGE.

#9


Define 1 to 1 function how do you test for one
Define 1 – to – 1 Function or not?How do you test for one?

#10


1 to 1 function a function whose inverse is also a function

1-to-1 Function: A function whose or not?inverse is also a function.

Horizontal Line Test

#10


How do you find an inverse function algebraically graphically

How do you find an INVERSE or not?Function… ALGEBRAICALLY?GRAPHICALLY?

#11


Algebraically: or not?Switch x and y… …solve for y.Graphically:Reflect over the line y=x (look at your table and switch x & y values)

#11


1.)What or not?notation do we use for Inverse?2.) Functions f and g are inverses of each other if _______ and ________!3.) If point (a,b) lies on f(x)…

#12


1.) Notation or not?:

2.) f(g(x)) = x and g(f(x)) = x

3.) …then point (b,a) lies on

#12


Shifts let f x x 2
SHIFTS or not?Let f(x) = x2

Describe the shift performed to f(x)

  • f(x) + a

  • f(x) – a

  • f(x+a)

  • f(x-a)

#13


#13


Complex numbers

COMPLEX NUMBERS or not?

YELLOW CARD


Explain how to simplify or not?

powers of i

#14


Divide the exponent by 4 remainder becomes the new exponent
Divide the exponent by 4. or not?Remainder becomes the new exponent.

#14



#15


How do you evaluate the absolute value magnitude of a complex number
How do you evaluate the ABSOLUTE VALUE (Magnitude) of a complex number?

|a + bi|

|2 – 5i|

#16


Pythagorean theorem
Pythagorean Theorem complex number?

|a + bi| = a2 + b2 = c2

|5 – 12i| = 13

#16



Discriminant
DISCRIMINANT… complex number?

#17


POSITIVE, complex number?

PERFECT SQUARE?

#18


Roots real rational unequal
ROOTS = complex number?Real, Rational, Unequal

  • Graph crosses the x-axis twice.

#18


POSITIVE, complex number?

NON-PERFECT SQUARE

#19


Roots real irrational unequal
ROOTS = complex number?Real, Irrational, Unequal

  • Graph still crosses x-axis twice

#19


ZERO complex number?

#20


Roots real rational equal
ROOTS = complex number?Real, Rational, Equal

  • GRAPH IS TANGENT TO THE X-AXIS.

#20


NEGATIVE complex number?

#21


Roots imaginary
ROOTS = complex number?IMAGINARY

  • GRAPH NEVER CROSSES THE

    X-AXIS.

#21


What is the sum of the roots what is the product of the roots
What is the SUM of the roots? complex number?What is the PRODUCT of the roots?

#22


  • SUM = complex number?

  • PRODUCT =

#22



#23


Multiplicative inverse
Multiplicative Inverse complex number?

#24


#24


Additive inverse
Additive Inverse complex number?

#25


#25


Inequalities and Absolute Value complex number?

Green card


Solve Absolute Value … complex number?

#26


  • Split into 2 branches complex number?

  • Only negate what is inside the absolute value on negative branch.

  • CHECK!!!!!

#26


Quadratic Inequalities… complex number?

#27


#27


Solve Radical Equations … complex number?

#28


#28


Rational expressions pink card
Rational Expressions complex number?pink card


Multiplying dividing rational expressions
Multiplying complex number?&Dividing Rational Expressions

#29


#29


Adding subtracting rational expressions
Adding complex number?&Subtracting Rational Expressions

#30


#30


Rational equations
Rational Equations complex number?

#31


#31


Complex fractions
Complex Fractions complex number?

#32


#32


Irrational expressions
Irrational Expressions complex number?


Conjugate
Conjugate complex number?

#33


#33


Rationalize the denominator
Rationalize the denominator complex number?

#34



Multiplying dividing radicals
Multiplying complex number?&Dividing Radicals

#35


#35


Adding subtracting radicals
Adding complex number?& Subtracting Radicals

#36


#36


Exponents
Exponents complex number?


When you multiply… complex number?

the base and

the exponents

#37


  • KEEP complex number? (the base)

  • ADD (the exponents)

#37


When dividing the base the exponents
When dividing… complex number? the base& the exponents.

#38


  • Keep complex number? (the base)

  • SUBTRACT (the exponents)

#38


Power to a power
Power to a power… complex number?

#39


#39


Negative exponents
Negative Exponents… complex number?

#40


#40


Ground hog rule
Ground Hog Rule complex number?

#41


#41 complex number?


Exponential equations y a b x identify the meaning of a b
Exponential Equations complex number?y = a(b)xIdentify the meaning of a & b

#42


#42



1 get a common base set the exponents equal 2 take the log of both sides
1. Get a variablecommon base, set the exponents equal2. Take the log of both sides

#43


A typical exponential graph looks like
A typical variableEXPONENTIAL GRAPH looks like…

#44




Example:

#45


Logarithms
Logarithms variable


Expand 1 log ab 2 log a b
Expand variable1) Log (ab) 2) Log(a+b)

#46


1 log a log b 2 done
1. log(a) + log (b) variable2. Done!

#46


Expand 1 log a b 2 log a b
Expand variable1. log (a/b)2. log (a-b)

#47


1 log a log b 2 done1
1. log(a) – log(b) variable2. DONE!!

#47


Expand 1 logx m
Expand variable1. logxm

#48


M log x
m log x variable

#48



#49 variable



Follow the arrows. variable

#50


Log equations 1 every term has a log 2 not all terms have a log
Log Equations variable1. every term has a log2. not all terms have a log

#51


1. Apply log properties and knock out all the logs variable2. Apply log properties condense log equationconvert to exponential and solve

#51




Change of base formula what is it used for
Change of Base Formula variableWhat is it used for?

#53


Used to graph logs
Used to graph logs variable

#53



Probability formula
Probability Formula… variable

At least 4 out of 6

At most 2 out of 6

#54


At least 4 out of 6 variable

4 or 5 or 6

At most 2

2 or 1 or 0

#54


Binomial theorem
Binomial Theorem variable

#55


Watch your signs
Watch your SIGNS!! variable

#55


Summation
Summation variable

#56



Normal distribution
Normal Distribution variable

  • What percentage lies within 1 S.D.?

  • What percentage lies within 2 S.D.?

  • What percentage lies within 3 S.D.?

#57


#57


Permutation or combination
Permutation variableor combination

#58


Permutation order is important ex position placement combination order is not important ex teams
Permutation – order is important variableex: position, placementCombination: order is not importantex: teams,

#58


Mean standard deviation
Mean variable&Standard deviation

#59


Mean stat 1 var stats
= mean. Stat/1 variablevar stats

Population standard deviation

sample standard deviation

#59


Varience
Varience variable

#60




Sin 30 or sin
sin 30 variableorsin

#61


# variable61


Sin 60 or sin
sin 60 variableorsin

#62


# variable62


Sin 45 or sin
sin 45 variableorsin

#63


# variable63


Sin 0
sin 0 variable

#64


0 variable

#64


Sin 90 or sin
sin 90 variableor sin

#65


1 variable

#65


Sin 180 or sin
sin 180 variableorsin

#66


0 variable

#66


Sin 270 or sin
sin 270 variableor sin

#67


-1 variable

#67


Sin 360 or sin
sin 360 variableor sin

#68


0 variable

#68


Cos 30 or cos
cos 30 variableor cos

#69


#69 variable


Cos 60 or cos
cos 60 variableorcos

#70


# variable70


Cos 45 or cos
cos 45 variableor cos

#71


# variable71


Cos 0
cos 0 variable

#72


1 variable

#72


Cos 90 or cos
cos 90 variableor cos

#73


0 variable

#73


Cos 180 or cos
cos 180 variableor cos

#74


-1 variable

#74


Cos 270 or cos
cos 270 variableor cos

#75


0 variable

#75


Cos 360 or cos
cos 360 variableor cos

#76


1 variable

#76


Tan 30 or tan
tan 30 variableor tan

#77


#77 variable


Tan 60 or tan
tan 60 variableor tan

#78


#78 variable


tan 45 variableor tan

#79


1 variable

#79


Tan 0
tan 0 variable

#80


0 variable

#80


tan 90 variableor tan

#81


D n e or undefined
D.N.E. variableorUndefined

#81


tan 180 variableor tan

#82


0 variable

#82


tan 270 variableor

tan

#83


D.N.E. variable

Or

Undefined

#83


tan 360 variableor tan

#84


0 variable

#84


Trig graphs
Trig Graphs variable


Amplitude
Amplitude variable

#85


Height from the midline y asin fx y 2sinx amp 2
Height from the midline variabley = asin(fx)y = -2sinxamp = 2

#85


Frequency
Frequency variable

#86



Period
Period variable

#87



Y sinx a graph b amplitude c frequency d period e domain f range
y = sinx variablea) graph b) amplitudec) frequencyd) periode) domain f) range

#88


A b 1 c 1 d e all real numbers f
a) variableb) 1c) 1d)e) all real numbersf)

#88


Y cosx a graph b amplitude c frequency d period e domain f range
y = cosx variablea) graph b) amplitudec) frequencyd) periode) domain f) range

#89


A b 1 c 1 d e all real numbers f1
a) variableb) 1c) 1d)e) all real numbersf)

#89


Y tan x a graph b amplitude c asymptotes at
y = tan x variablea) graphb) amplitudec) asymptotes at…

#90


A b no amplitude c asymptotes are at odd multiplies of
a) variableb) No amplitudec) Asymptotes are at odd multiplies of

Graph is always increasing

#90


Y csc x
y = csc x variable

  • A) graph

  • B) location of the asymptotes

#91


B asymptotes are multiples of
b) variableAsymptotes are multiples of

Draw in ghost sketch

#91


Y secx
y = secx variable

  • A) graph

  • B) location of the asymptotes

#92


Draw in ghost sketch variable

  • B) asymptotes are odd multiples of

#92


Y cotx
y=cotx variable

  • A) graph

  • B) location of asymptotes

#93


#93


Vertical shifts f x asin fx c
Vertical Shifts variablef(x) = asin(fx) + c

#94


Identify the vertical shift draw a ghost sketch of the midline
* Identify the vertical shift. variableDraw a ghost sketch of the midline.

amplitude

Freq = 1

1 cycle till 2pi

midline

#94


Horizontal shift f x asin fx b c
Horizontal variable Shift f(x) = asin(fx+b) + c

#95


• Horizontal Shifts go in the variableopposite directionSTEPS: Ignore the shift, make a ghost sketch then apply the shift!

Graph y = cos(x-pi) + 3

Now shift your graph over pi and redraw! y = cos(x-pi) + 3

1st graph y = cosx + 3

#95


Y sin 1 x or y arcsinx
y = sin variable-1xor y = arcsinx

Sketch graph

State domain

#96


Domain
Domain variable

Quadrants I & IV

#96


  • y = tan-1xor y = arctanx

#97


Domain variable

Quadrants I & IV

#97


Y cos 1 x or y arccosx
y = cos variable-1xor y = arccosx

  • State domain

  • Sketch graph

#98


Domain variable

Quadrants I & II

#98



Reciprocal identity
Reciprocal Identity variable

sec =

#99


# variable99


Reciprocal identity1
Reciprocal Identity variable

csc =

#100


#100 variable


Reciprocal Identity variable

cot =

#101


#101 variable


Quotient identity
Quotient Identity variable

#102


#102 variable


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