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# Algebra II TRIG Flashcards - PowerPoint PPT Presentation

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

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.

• 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?

• Pink Card

### Vertex Formula(Axis of Symmetry)

What is it good for?

#1

Axis of symmetry

#1

What is it good for?

#2

(x-intercepts).

#2

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 VARIATIONCharacteristics & Sketch

#4

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

#4

Define Inverse Variation

#5

Give a real life example

#5

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

#6

xy = k or . (constant

HYPERBOLA (ROTATED)

#6

#7 (constant

### FUNCTIONS (constant

BLUE CARD

Define Domain (constantDefine Range

#8

#8

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 or not?How do you test for one?

#10

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

Horizontal Line Test

#10

### 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 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 or not?

YELLOW CARD

Explain how to simplify or not?

powers of i

#14

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

#14

### Describe How to Graph Complex Numbers or not?

#15

#15

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

|a + bi|

|2 – 5i|

#16

Pythagorean Theorem complex number?

|a + bi| = a2 + b2 = c2

|5 – 12i| = 13

#16

DISCRIMINANT… complex number?

#17

POSITIVE, complex number?

PERFECT SQUARE?

#18

ROOTS = complex number?Real, Rational, Unequal

• Graph crosses the x-axis twice.

#18

POSITIVE, complex number?

NON-PERFECT SQUARE

#19

ROOTS = complex number?Real, Irrational, Unequal

• Graph still crosses x-axis twice

#19

ZERO complex number?

#20

ROOTS = complex number?Real, Rational, Equal

• GRAPH IS TANGENT TO THE X-AXIS.

#20

NEGATIVE complex number?

#21

ROOTS = complex number?IMAGINARY

• GRAPH NEVER CROSSES THE

X-AXIS.

#21

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 complex number?

#24

#24

#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

#27

#27

Solve Radical Equations … complex number?

#28

#28

Rational Expressions complex number?pink card

Multiplying complex number?&Dividing Rational Expressions

#29

#29

#30

#30

Rational Equations complex number?

#31

#31

Complex Fractions complex number?

#32

#32

Irrational Expressions complex number?

Conjugate complex number?

#33

#33

Rationalize the denominator complex number?

#34

#35

#35

#36

#36

Exponents complex number?

When you multiply… complex number?

the base and

the exponents

#37

• KEEP complex number? (the base)

#37

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

#38

• Keep complex number? (the base)

• SUBTRACT (the exponents)

#38

Power to a power… complex number?

#39

#39

Negative Exponents… complex number?

#40

#40

Ground Hog Rule complex number?

#41

#41 complex number?

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

#42

#42

#43

1. Get a variablecommon base, set the exponents equal2. Take the log of both sides

#43

A typical variableEXPONENTIAL GRAPH looks like…

#44

#45

Example:

#45

Logarithms variable

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

#46

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

#46

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

#47

1. log(a) – log(b) variable2. DONE!!

#47

Expand variable1. logxm

#48

m log x variable

#48

#49 variable

#50

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

#52

Change of Base Formula variableWhat is it used for?

#53

Used to graph logs variable

#53

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 variable

#55

#55

Summation variable

#56

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 variableor combination

#58

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

#58

Mean variable&Standard deviation

#59

= mean. Stat/1 variablevar stats

Population standard deviation

sample standard deviation

#59

Varience variable

#60

sin 30 variableorsin

#61

# variable61

sin 60 variableorsin

#62

# variable62

sin 45 variableorsin

#63

# variable63

sin 0 variable

#64

0 variable

#64

sin 90 variableor sin

#65

1 variable

#65

sin 180 variableorsin

#66

0 variable

#66

sin 270 variableor sin

#67

-1 variable

#67

sin 360 variableor sin

#68

0 variable

#68

cos 30 variableor cos

#69

#69 variable

cos 60 variableorcos

#70

# variable70

cos 45 variableor cos

#71

# variable71

cos 0 variable

#72

1 variable

#72

cos 90 variableor cos

#73

0 variable

#73

cos 180 variableor cos

#74

-1 variable

#74

cos 270 variableor cos

#75

0 variable

#75

cos 360 variableor cos

#76

1 variable

#76

tan 30 variableor tan

#77

#77 variable

tan 60 variableor tan

#78

#78 variable

tan 45 variableor tan

#79

1 variable

#79

tan 0 variable

#80

0 variable

#80

tan 90 variableor tan

#81

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 variable

Amplitude variable

#85

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

#85

Frequency variable

#86

Period variable

#87

y = sinx variablea) graph b) amplitudec) frequencyd) periode) domain f) range

#88

a) variableb) 1c) 1d)e) all real numbersf)

#88

y = cosx variablea) graph b) amplitudec) frequencyd) periode) domain f) range

#89

a) variableb) 1c) 1d)e) all real numbersf)

#89

y = tan x variablea) graphb) amplitudec) asymptotes at…

#90

a) variableb) No amplitudec) Asymptotes are at odd multiplies of

Graph is always increasing

#90

y = csc x variable

• A) graph

• B) location of the asymptotes

#91

b) variableAsymptotes are multiples of

Draw in ghost sketch

#91

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 variable

• A) graph

• B) location of asymptotes

#93

#93

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

#94

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

amplitude

Freq = 1

1 cycle till 2pi

midline

#94

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 variable-1xor y = arcsinx

Sketch graph

State domain

#96

Domain variable

#96

• y = tan-1xor y = arctanx

#97

Domain variable

#97

y = cos variable-1xor y = arccosx

• State domain

• Sketch graph

#98

Domain variable

#98

Reciprocal Identity variable

sec =

#99

# variable99

Reciprocal Identity variable

csc =

#100

#100 variable

Reciprocal Identity variable

cot =

#101

#101 variable

Quotient Identity variable

#102

#102 variable