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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.

- 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

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

- 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

#4

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#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

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

#6

HYPERBOLA (ROTATED)

#6

General Form of a Circle

#7

#7

FUNCTIONS

BLUE CARD

#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

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

#9

#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

#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

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

#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

|a + bi|

|2 – 5i|

#16

|a + bi| = a2 + b2 = c2

|5 – 12i| = 13

#16

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#17

POSITIVE,

PERFECT SQUARE?

#18

- Graph crosses the x-axis twice.

#18

POSITIVE,

NON-PERFECT SQUARE

#19

- Graph still crosses x-axis twice

#19

ZERO

#20

- GRAPH IS TANGENT TO THE X-AXIS.

#20

NEGATIVE

#21

- GRAPH NEVER CROSSES THE
X-AXIS.

#21

#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

#24

- One over what ever is given.
- Don’t forget to RATIONALIZE
- Ex. Multiplicative inverse of 3 + i

#24

#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

#29

- Change Division to Multiplication flip the second fraction
- Factor
- Cancel (one on top with one on the bottom)

#29

#30

- FIRST change subtraction to addition
- Find a common denominator
- Simplify
- KEEP THE DENOMINATOR!!!!!!

#30

#31

- First find the common denominator
- Multiply every term by the common denominator
- “KILL THE FRACTION”
- Solve
- Check your answers

#31

#32

- Multiply every term by the common denominator
- Factor if necessary
- Simplify

#32

#33

- Change only the sign of the second term
- Ex. 4 + 3i
conjugate 4 – 3i

#33

#34

- Multiply the numerator and denominator by the CONJUGATE
- Simplify

#34

#35

- Multiply/divide the numbers outside the radical together
- Multiply/divide the numbers in side the radical together

#35

#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

When you multiply…

the base and

the exponents

#37

- KEEP (the base)
- ADD (the exponents)

#37

#38

- Keep (the base)
- SUBTRACT (the exponents)

#38

#39

- MULTIPLY the exponents

#39

#40

- Reciprocate the base

#40

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#41

#42

- Exponential equations occur when the exponent contains a variable
- a = initial amount
- b = growth factor
b > 1 Growth

b < 1 Decay

#42

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#43

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#44

#45

- Get x by itself.
- Raise both sides to the reciprocal.

Example:

#45

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#48

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#49

#50

Follow the arrows.

#50

#51

#51

#52

#52

#53

#53

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

#55

#55

#56

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

#56

- 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

#58

#58

#59

Population standard deviation

sample standard deviation

#59

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#78

tan 45or tan

#79

1

#79

#80

0

#80

tan 90or tan

#81

#81

tan 180or tan

#82

0

#82

tan 270or

tan

#83

D.N.E.

Or

Undefined

#83

tan 360or tan

#84

0

#84

#85

#85

#86

#86

#87

#87

#88

#88

#89

#89

#90

Graph is always increasing

#90

- A) graph
- B) location of the asymptotes

#91

Draw in ghost sketch

#91

- A) graph
- B) location of the asymptotes

#92

Draw in ghost sketch

- B) asymptotes are odd multiples of

#92

- A) graph
- B) location of asymptotes

#93

- B) multiplies of
- Always decreasing

#93

#94

amplitude

Freq = 1

1 cycle till 2pi

midline

#94

#95

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

Sketch graph

State domain

#96

Quadrants I & IV

#96

- State domain
- Sketch graph

- y = tan-1xor y = arctanx

#97

Domain

Quadrants I & IV

#97

- State domain
- Sketch graph

#98

Domain

Quadrants I & II

#98

Trigonometry Identities

sec =

#99

#99

csc =

#100

#100

Reciprocal Identity

cot =

#101

#101

#102

#102