Algebra ii trig flashcards
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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

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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?


Quadratic equations

Quadratic Equations

  • Pink Card


Vertex formula axis of symmetry

Vertex Formula(Axis of Symmetry)

What is it good for?

#1


Tells us the x coordinate of the maximum point axis of symmetry

Tells us the x-coordinate of the maximum point

Axis of symmetry

#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


Algebra ii trig flashcards

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


Algebra ii trig flashcards

  • The PRODUCT of two variables will always be the same (constant).

    xy=c

  • Example:

    • The speed, s, you drive and the time, t, it takes for you to get to Rochester.

#5


State the general form of an inverse variation equation

State the General Form of an inverse variation equation.

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

#6


Xy k or

xy = k or .

HYPERBOLA (ROTATED)

#6


Algebra ii trig flashcards

General Form of a Circle

#7


Algebra ii trig flashcards

#7


Functions

FUNCTIONS

BLUE CARD


Define domain define range

Define DomainDefine Range

#8


Algebra ii trig flashcards

  • DOMAIN - List of all possible x-values

    (aka – List of what x is allowed to be).

  • RANGE – List of all possible y-values.

#8


Algebra ii trig flashcards

Test whether a relation (any random equation) is a FUNCTION or not?

#9


Vertical line test

Vertical Line Test

  • 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 FunctionHow 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 inverse is also a function.

Horizontal Line Test

#10


How do you find an inverse function algebraically graphically

How do you find an INVERSE Function… ALGEBRAICALLY?GRAPHICALLY?

#11


Algebra ii trig flashcards

Algebraically:Switch x and y……solve for y.Graphically:Reflect over the line y=x (look at your table and switch x & y values)

#11


Algebra ii trig flashcards

1.)What 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


Algebra ii trig flashcards

1.) Notation:

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

3.) …then point (b,a) lies on

#12


Shifts let f x x 2

SHIFTSLet f(x) = x2

Describe the shift performed to f(x)

  • f(x) + a

  • f(x) – a

  • f(x+a)

  • f(x-a)

#13


Algebra ii trig flashcards

  • f(x) + a = shift ‘a’ units upward

  • f(x) – a = shift ‘a’ units down.

  • f(x+a) = shift ‘a’ units to the left.

  • f(x-a) = shift ‘a’ units to the right.

#13


Complex numbers

COMPLEX NUMBERS

YELLOW CARD


Algebra ii trig flashcards

Explain how to simplify

powers of i

#14


Divide the exponent by 4 remainder becomes the new exponent

Divide the exponent by 4.Remainder becomes the new exponent.

#14


Describe how to graph complex numbers

Describe How to Graph Complex Numbers

#15


Algebra ii trig flashcards

  • x-axis represents real numbers

  • y-axis represents imaginary numbers

  • Plot point and draw vector from origin.

#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

|a + bi| = a2 + b2 = c2

|5 – 12i| = 13

#16


How do you identify the nature of the roots

How do you identify the NATURE OF THE ROOTS?

#17


Discriminant

DISCRIMINANT…

#17


Algebra ii trig flashcards

POSITIVE,

PERFECT SQUARE?

#18


Roots real rational unequal

ROOTS = Real, Rational, Unequal

  • Graph crosses the x-axis twice.

#18


Algebra ii trig flashcards

POSITIVE,

NON-PERFECT SQUARE

#19


Roots real irrational unequal

ROOTS = Real, Irrational, Unequal

  • Graph still crosses x-axis twice

#19


Algebra ii trig flashcards

ZERO

#20


Roots real rational equal

ROOTS = Real, Rational, Equal

  • GRAPH IS TANGENT TO THE X-AXIS.

#20


Algebra ii trig flashcards

NEGATIVE

#21


Roots imaginary

ROOTS = 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?What is the PRODUCT of the roots?

#22


Algebra ii trig flashcards

  • SUM =

  • PRODUCT =

#22


Algebra ii trig flashcards

How do you write a quadratic equation given the roots?

#23


Algebra ii trig flashcards

  • Find the SUM of the roots

  • Find the PRODUCT of the roots

#23


Multiplicative inverse

Multiplicative Inverse

#24


Algebra ii trig flashcards

  • One over what ever is given.

  • Don’t forget to RATIONALIZE

  • Ex. Multiplicative inverse of 3 + i

#24


Additive inverse

Additive Inverse

#25


Algebra ii trig flashcards

  • What you add to, to get 0.

  • Additive inverse of -3 + 4i is

    3 – 4i

#25


Algebra ii trig flashcards

Inequalities and Absolute Value

Green card


Algebra ii trig flashcards

Solve Absolute Value …

#26


Algebra ii trig flashcards

  • Split into 2 branches

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

  • CHECK!!!!!

#26


Algebra ii trig flashcards

Quadratic Inequalities…

#27


Algebra ii trig flashcards

  • Factor and find the roots like normal

  • Make sign chart

  • Graph solution on a number line (shade where +)

#27


Algebra ii trig flashcards

Solve Radical Equations …

#28


Algebra ii trig flashcards

  • Isolate the radical

  • Square both sides

  • Solve

  • CHECK!!!!!!!!!

#28


Rational expressions pink card

Rational Expressionspink card


Multiplying dividing rational expressions

Multiplying &Dividing Rational Expressions

#29


Algebra ii trig flashcards

  • Change Division to Multiplication flip the second fraction

  • Factor

  • Cancel (one on top with one on the bottom)

#29


Adding subtracting rational expressions

Adding&Subtracting Rational Expressions

#30


Algebra ii trig flashcards

  • FIRST change subtraction to addition

  • Find a common denominator

  • Simplify

  • KEEP THE DENOMINATOR!!!!!!

#30


Rational equations

Rational Equations

#31


Algebra ii trig flashcards

  • First find the common denominator

  • Multiply every term by the common denominator

  • “KILL THE FRACTION”

  • Solve

  • Check your answers

#31


Complex fractions

Complex Fractions

#32


Algebra ii trig flashcards

  • Multiply every term by the common denominator

  • Factor if necessary

  • Simplify

#32


Irrational expressions

Irrational Expressions


Conjugate

Conjugate

#33


Algebra ii trig flashcards

  • Change only the sign of the second term

  • Ex. 4 + 3i

    conjugate 4 – 3i

#33


Rationalize the denominator

Rationalize the denominator

#34


Algebra ii trig flashcards

  • Multiply the numerator and denominator by the CONJUGATE

  • Simplify

#34


Multiplying dividing radicals

Multiplying &Dividing Radicals

#35


Algebra ii trig flashcards

  • Multiply/divide the numbers outside the radical together

  • Multiply/divide the numbers in side the radical together

#35


Adding subtracting radicals

Adding & Subtracting Radicals

#36


Algebra ii trig flashcards

  • Only add and subtract “LIKE RADICALS”

  • The numbers under the radical must be the same.

  • ADD/SUBTRACT the numbers outside the radical. Keep the radical

#36


Exponents

Exponents


Algebra ii trig flashcards

When you multiply…

the base and

the exponents

#37


Algebra ii trig flashcards

  • KEEP (the base)

  • ADD (the exponents)

#37


When dividing the base the exponents

When dividing… the base& the exponents.

#38


Algebra ii trig flashcards

  • Keep (the base)

  • SUBTRACT (the exponents)

#38


Power to a power

Power to a power…

#39


Algebra ii trig flashcards

  • MULTIPLY the exponents

#39


Negative exponents

Negative Exponents…

#40


Algebra ii trig flashcards

  • Reciprocate the base

#40


Ground hog rule

Ground Hog Rule

#41


Algebra ii trig flashcards

#41


Exponential equations y a b x identify the meaning of a b

Exponential Equationsy = a(b)xIdentify the meaning of a & b

#42


Algebra ii trig flashcards

  • Exponential equations occur when the exponent contains a variable

  • a = initial amount

  • b = growth factor

    b > 1 Growth

    b < 1 Decay

#42


Name 2 ways to solve an exponential equation

Name 2 ways to solve an Exponential Equation

#43


1 get a common base set the exponents equal 2 take the log of both sides

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

#43


A typical exponential graph looks like

A typical EXPONENTIAL GRAPH looks like…

#44


Horizontal asymptote y 0

Horizontal asymptote y = 0

#44


Solving equations with fractional exponents

Solving Equations with Fractional Exponents

#45


Algebra ii trig flashcards

  • Get x by itself.

  • Raise both sides to the reciprocal.

Example:

#45


Logarithms

Logarithms


Expand 1 log ab 2 log a b

Expand1) Log (ab) 2) Log(a+b)

#46


1 log a log b 2 done

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

#46


Expand 1 log a b 2 log a b

Expand1. log (a/b)2. log (a-b)

#47


1 log a log b 2 done1

1. log(a) – log(b)2. DONE!!

#47


Expand 1 logx m

Expand1. logxm

#48


M log x

m log x

#48


Convert exponential to log form 2 3 8

Convert exponential to log form23 = 8

#49


Algebra ii trig flashcards

#49


Convert log form to exponential form log 2 8 3

Convert log form to exponential formlog28 = 3

#50


Algebra ii trig flashcards

Follow the arrows.

#50


Log equations 1 every term has a log 2 not all terms have a log

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

#51


Algebra ii trig flashcards

1. Apply log properties and knock out all the logs2. Apply log properties condense log equationconvert to exponential and solve

#51


What does a typical logarithmic graph look like

What does a typical logarithmic graph look like?

#52


Vertical asymptote at x 0

Vertical asymptote at x = 0

#52


Change of base formula what is it used for

Change of Base FormulaWhat is it used for?

#53


Used to graph logs

Used to graph logs

#53


Probability and statistics

Probability and Statistics


Probability formula

Probability Formula…

At least 4 out of 6

At most 2 out of 6

#54


Algebra ii trig flashcards

At least 4 out of 6

4or5or6

At most 2

2or1 or0

#54


Binomial theorem

Binomial Theorem

#55


Watch your signs

Watch your SIGNS!!

#55


Summation

Summation

#56


Algebra ii trig flashcards

  • "The summation from 1 to 4 of 3n":

#56


Normal distribution

Normal Distribution

  • What percentage lies within 1 S.D.?

  • What percentage lies within 2 S.D.?

  • What percentage lies within 3 S.D.?

#57


Algebra ii trig flashcards

  • What percentage lies within 1 S.D.?

    68%

  • What percentage lies within 2 S.D.?

    95%

  • What percentage lies within 3 S.D.?

    99%

#57


Permutation or combination

Permutation or combination

#58


Permutation order is important ex position placement combination order is not important ex teams

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

#58


Mean standard deviation

Mean&Standard deviation

#59


Mean stat 1 var stats

= mean. Stat/1 var stats

Population standard deviation

sample standard deviation

#59


Varience

Varience

#60


Standard deviation squared

Standard deviation squared

#60


Exact trig values

EXACT TRIG VALUES


Sin 30 or sin

sin 30orsin

#61


Algebra ii trig flashcards

#61


Sin 60 or sin

sin 60orsin

#62


Algebra ii trig flashcards

#62


Sin 45 or sin

sin 45orsin

#63


Algebra ii trig flashcards

#63


Sin 0

sin 0

#64


Algebra ii trig flashcards

0

#64


Sin 90 or sin

sin 90or sin

#65


Algebra ii trig flashcards

1

#65


Sin 180 or sin

sin 180orsin

#66


Algebra ii trig flashcards

0

#66


Sin 270 or sin

sin 270or sin

#67


Algebra ii trig flashcards

-1

#67


Sin 360 or sin

sin 360or sin

#68


Algebra ii trig flashcards

0

#68


Cos 30 or cos

cos 30or cos

#69


Algebra ii trig flashcards

#69


Cos 60 or cos

cos 60orcos

#70


Algebra ii trig flashcards

#70


Cos 45 or cos

cos 45or cos

#71


Algebra ii trig flashcards

#71


Cos 0

cos 0

#72


Algebra ii trig flashcards

1

#72


Cos 90 or cos

cos 90or cos

#73


Algebra ii trig flashcards

0

#73


Cos 180 or cos

cos 180 or cos

#74


Algebra ii trig flashcards

-1

#74


Cos 270 or cos

cos 270 or cos

#75


Algebra ii trig flashcards

0

#75


Cos 360 or cos

cos 360or cos

#76


Algebra ii trig flashcards

1

#76


Tan 30 or tan

tan 30or tan

#77


Algebra ii trig flashcards

#77


Tan 60 or tan

tan 60or tan

#78


Algebra ii trig flashcards

#78


Algebra ii trig flashcards

tan 45or tan

#79


Algebra ii trig flashcards

1

#79


Tan 0

tan 0

#80


Algebra ii trig flashcards

0

#80


Algebra ii trig flashcards

tan 90or tan

#81


D n e or undefined

D.N.E.orUndefined

#81


Algebra ii trig flashcards

tan 180or tan

#82


Algebra ii trig flashcards

0

#82


Algebra ii trig flashcards

tan 270or

tan

#83


Algebra ii trig flashcards

D.N.E.

Or

Undefined

#83


Algebra ii trig flashcards

tan 360or tan

#84


Algebra ii trig flashcards

0

#84


Trig graphs

Trig Graphs


Amplitude

Amplitude

#85


Height from the midline y asin fx y 2sinx amp 2

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

#85


Frequency

Frequency

#86


How many complete cycles between 0 and

How many complete cycles between 0 and

#86


Period

Period

#87


How long it takes to complete one full cycle formula

How long it takes to complete one full cycleFormula:

#87


Y sinx a graph b amplitude c frequency d period e domain f range

y = sinxa) graph b) amplitudec) frequencyd) periode) domain f) range

#88


A b 1 c 1 d e all real numbers f

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

#88


Y cosx a graph b amplitude c frequency d period e domain f range

y = cosxa) graph b) amplitudec) frequencyd) periode) domain f) range

#89


A b 1 c 1 d e all real numbers f1

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

#89


Y tan x a graph b amplitude c asymptotes at

y = tan xa) graphb) amplitudec) asymptotes at…

#90


A b no amplitude c asymptotes are at odd multiplies of

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

Graph is always increasing

#90


Y csc x

y = csc x

  • A) graph

  • B) location of the asymptotes

#91


B asymptotes are multiples of

b) Asymptotes are multiples of

Draw in ghost sketch

#91


Y secx

y = secx

  • A) graph

  • B) location of the asymptotes

#92


Algebra ii trig flashcards

Draw in ghost sketch

  • B) asymptotes are odd multiples of

#92


Y cotx

y=cotx

  • A) graph

  • B) location of asymptotes

#93


Algebra ii trig flashcards

  • B) multiplies of

  • Always decreasing

#93


Vertical shifts f x asin fx c

Vertical Shiftsf(x) = asin(fx) + c

#94


Identify the vertical shift draw a ghost sketch of the midline

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

amplitude

Freq = 1

1 cycle till 2pi

midline

#94


Horizontal shift f x asin fx b c

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

#95


Algebra ii trig flashcards

• Horizontal Shifts go in the opposite 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-1xor y = arcsinx

Sketch graph

State domain

#96


Domain

Domain

Quadrants I & IV

#96


Algebra ii trig flashcards

  • State domain

  • Sketch graph

  • y = tan-1xor y = arctanx

#97


Algebra ii trig flashcards

Domain

Quadrants I & IV

#97


Y cos 1 x or y arccosx

y = cos-1xor y = arccosx

  • State domain

  • Sketch graph

#98


Algebra ii trig flashcards

Domain

Quadrants I & II

#98


Algebra ii trig flashcards

Trigonometry Identities


Reciprocal identity

Reciprocal Identity

sec =

#99


Algebra ii trig flashcards

#99


Reciprocal identity1

Reciprocal Identity

csc =

#100


Algebra ii trig flashcards

#100


Algebra ii trig flashcards

Reciprocal Identity

cot =

#101


Algebra ii trig flashcards

#101


Quotient identity

Quotient Identity

#102


Algebra ii trig flashcards

#102


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