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

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?

  • 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

  • Pink Card


Vertex Formula(Axis of Symmetry)

What is it good for?

#1


Tells us the x-coordinate of the maximum point

Axis of symmetry

#1


Quadratic Formula

What is it good for?

#2


Tells us the roots

(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


  • 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.

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

#6


xy = k or .

HYPERBOLA (ROTATED)

#6


General Form of a Circle

#7


#7


FUNCTIONS

BLUE CARD


Define DomainDefine Range

#8


  • DOMAIN - List of all possible x-values

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

  • RANGE – List of all possible y-values.

#8


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

#9


Vertical Line Test

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

#9


Define 1 – to – 1 FunctionHow do you test for one?

#10


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?

#11


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


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


1.) Notation:

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

3.) …then point (b,a) lies on

#12


SHIFTSLet f(x) = x2

Describe the shift performed to f(x)

  • f(x) + a

  • f(x) – a

  • f(x+a)

  • f(x-a)

#13


  • 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

YELLOW CARD


Explain how to simplify

powers of i

#14


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

#14


Describe How to Graph Complex Numbers

#15


  • 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?

|a + bi|

|2 – 5i|

#16


Pythagorean Theorem

|a + bi| = a2 + b2 = c2

|5 – 12i| = 13

#16


How do you identify the NATURE OF THE ROOTS?

#17


DISCRIMINANT…

#17


POSITIVE,

PERFECT SQUARE?

#18


ROOTS = Real, Rational, Unequal

  • Graph crosses the x-axis twice.

#18


POSITIVE,

NON-PERFECT SQUARE

#19


ROOTS = Real, Irrational, Unequal

  • Graph still crosses x-axis twice

#19


ZERO

#20


ROOTS = Real, Rational, Equal

  • GRAPH IS TANGENT TO THE X-AXIS.

#20


NEGATIVE

#21


ROOTS = IMAGINARY

  • GRAPH NEVER CROSSES THE

    X-AXIS.

#21


What is the SUM of the roots?What is the PRODUCT of the roots?

#22


  • SUM =

  • PRODUCT =

#22


How do you write a quadratic equation given the roots?

#23


  • Find the SUM of the roots

  • Find the PRODUCT of the roots

#23


Multiplicative Inverse

#24


  • One over what ever is given.

  • Don’t forget to RATIONALIZE

  • Ex. Multiplicative inverse of 3 + i

#24


Additive Inverse

#25


  • What you add to, to get 0.

  • Additive inverse of -3 + 4i is

    3 – 4i

#25


Inequalities and Absolute Value

Green card


Solve Absolute Value …

#26


  • Split into 2 branches

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

  • CHECK!!!!!

#26


Quadratic Inequalities…

#27


  • Factor and find the roots like normal

  • Make sign chart

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

#27


Solve Radical Equations …

#28


  • Isolate the radical

  • Square both sides

  • Solve

  • CHECK!!!!!!!!!

#28


Rational Expressionspink card


Multiplying &Dividing Rational Expressions

#29


  • Change Division to Multiplication flip the second fraction

  • Factor

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

#29


Adding&Subtracting Rational Expressions

#30


  • FIRST change subtraction to addition

  • Find a common denominator

  • Simplify

  • KEEP THE DENOMINATOR!!!!!!

#30


Rational Equations

#31


  • First find the common denominator

  • Multiply every term by the common denominator

  • “KILL THE FRACTION”

  • Solve

  • Check your answers

#31


Complex Fractions

#32


  • Multiply every term by the common denominator

  • Factor if necessary

  • Simplify

#32


Irrational Expressions


Conjugate

#33


  • Change only the sign of the second term

  • Ex. 4 + 3i

    conjugate 4 – 3i

#33


Rationalize the denominator

#34


  • Multiply the numerator and denominator by the CONJUGATE

  • Simplify

#34


Multiplying &Dividing Radicals

#35


  • Multiply/divide the numbers outside the radical together

  • Multiply/divide the numbers in side the radical together

#35


Adding & Subtracting Radicals

#36


  • 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


When you multiply…

the base and

the exponents

#37


  • KEEP (the base)

  • ADD (the exponents)

#37


When dividing… the base& the exponents.

#38


  • Keep (the base)

  • SUBTRACT (the exponents)

#38


Power to a power…

#39


  • MULTIPLY the exponents

#39


Negative Exponents…

#40


  • Reciprocate the base

#40


Ground Hog Rule

#41


#41


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

#42


  • 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

#43


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

#43


A typical EXPONENTIAL GRAPH looks like…

#44


Horizontal asymptote y = 0

#44


Solving Equations with Fractional Exponents

#45


  • Get x by itself.

  • Raise both sides to the reciprocal.

Example:

#45


Logarithms


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

#46


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

#46


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

#47


1. log(a) – log(b)2. DONE!!

#47


Expand1. logxm

#48


m log x

#48


Convert exponential to log form23 = 8

#49


#49


Convert log form to exponential formlog28 = 3

#50


Follow the arrows.

#50


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

#51


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?

#52


Vertical asymptote at x = 0

#52


Change of Base FormulaWhat is it used for?

#53


Used to graph logs

#53


Probability and Statistics


Probability Formula…

At least 4 out of 6

At most 2 out of 6

#54


At least 4 out of 6

4or5or6

At most 2

2or1 or0

#54


Binomial Theorem

#55


Watch your SIGNS!!

#55


Summation

#56


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

#56


Normal Distribution

  • What percentage lies within 1 S.D.?

  • What percentage lies within 2 S.D.?

  • What percentage lies within 3 S.D.?

#57


  • 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

#58


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

#58


Mean&Standard deviation

#59


= mean. Stat/1 var stats

Population standard deviation

sample standard deviation

#59


Varience

#60


Standard deviation squared

#60


EXACT TRIG VALUES


sin 30orsin

#61


#61


sin 60orsin

#62


#62


sin 45orsin

#63


#63


sin 0

#64


0

#64


sin 90or sin

#65


1

#65


sin 180orsin

#66


0

#66


sin 270or sin

#67


-1

#67


sin 360or sin

#68


0

#68


cos 30or cos

#69


#69


cos 60orcos

#70


#70


cos 45or cos

#71


#71


cos 0

#72


1

#72


cos 90or cos

#73


0

#73


cos 180 or cos

#74


-1

#74


cos 270 or cos

#75


0

#75


cos 360or cos

#76


1

#76


tan 30or tan

#77


#77


tan 60or tan

#78


#78


tan 45or tan

#79


1

#79


tan 0

#80


0

#80


tan 90or tan

#81


D.N.E.orUndefined

#81


tan 180or tan

#82


0

#82


tan 270or

tan

#83


D.N.E.

Or

Undefined

#83


tan 360or tan

#84


0

#84


Trig Graphs


Amplitude

#85


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

#85


Frequency

#86


How many complete cycles between 0 and

#86


Period

#87


How long it takes to complete one full cycleFormula:

#87


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

#88


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

#88


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

#89


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

#89


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

#90


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

Graph is always increasing

#90


y = csc x

  • A) graph

  • B) location of the asymptotes

#91


b) Asymptotes are multiples of

Draw in ghost sketch

#91


y = secx

  • A) graph

  • B) location of the asymptotes

#92


Draw in ghost sketch

  • B) asymptotes are odd multiples of

#92


y=cotx

  • A) graph

  • B) location of asymptotes

#93


  • B) multiplies of

  • Always decreasing

#93


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

#94


* 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

#95


• 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-1xor y = arcsinx

Sketch graph

State domain

#96


Domain

Quadrants I & IV

#96


  • State domain

  • Sketch graph

  • y = tan-1xor y = arctanx

#97


Domain

Quadrants I & IV

#97


y = cos-1xor y = arccosx

  • State domain

  • Sketch graph

#98


Domain

Quadrants I & II

#98


Trigonometry Identities


Reciprocal Identity

sec =

#99


#99


Reciprocal Identity

csc =

#100


#100


Reciprocal Identity

cot =

#101


#101


Quotient Identity

#102


#102


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