Show Menu
Cheatography
  1. Home >
  2. Education >

Algebra II Final Cheat Sheet by

For the use of Algebra II Final

Periodic Functions

Periodic Function: repeats a pattern of y-values (outputs) at regular intervals

Cycle: may begin at any point in a graph

Period: is the horizontal length of one cycle.

Special Right Angles

45-45-90
h = sqrt 2 times l

30-60-90
h = 2 times s
l = sqrt 3 times s
s = short leg
l = long leg

Properties Of Sine Functions

y = a sin b theta

period = 2pi/b
|a| = amplitude
b = number of cycles (0 to 2pi)

Quadratic Functions

Standard Form

f(x) = ax2 + bx + c
ax2
Quadratic term

bx
Linear term

c
constant term

Expone­ntial Growth & Expone­ntial Decay

b= 1 + r
b>1 = epon. growth

When b<1, b is a decay factor
x-axis = asymptote
0<b­<1
b= 1+(-r)
y=abx
b= growth factor
r= increase in rate

e & Its Import­ance

A = Pert
A= amount in account
P=prin­cipal (what you start with)
r = rate in interest (annually)
t= time (in years)
  

Unit Circle

radian 2pi, tangent 0
radian pi/6, tangent sqrt 3/3
radian pi/4, tangent 1
radian pi/3, tangent sqrt 3
radian pi/2, tangent undefined
radian 2pi/3, tangent -sqrt 3
radian 3pi/4, tangent -1
radian 5pi/6, tangent -sqrt3/3
radian pi, tangent 0
radian 7pi/6, tangent sqrt3/3
radian 5pi/4, tangent 1
radian 4pi/3, tangent sqrt3
radian 3pi/2, tangent undefined
radian 5pi/3, tangent -sqrt3
radian 7pi/4, tangent -1
radian 11pi/6, tangent sqrt3/3

Sine, Cosine, Tangent

Sine = opp./adj.

Cosine = Adj./Hypo.

Tangent = Opp./Adj.

Mazimun & Minimum

y = ax2+bx+c
AOS: = x = -b/2a

1. vertex
2. c
3. another point
Area= length times width
  

Trigon­ometric Identities

Reciprocal Identities
csc theta = 1/sin theta

Sec theta = 1/ cos theta

Cot theta = 1/ tan theta

Tangent & Cotangent Identities
Tan theta = sin theta/ cos theta

Cot theta = cos theta/ sin theta

Pythag­orean Identities
Cos2 theta + Sin2 theta = 1

1+ Tan 2 theta = Sec2 theta

1+ Cot2 theta = Csc2 theta

Angle Identities

Angle Difference Identities
sin (A-B) = sinA cosB-cosA sinB

cos (A-B) = cosA cosB + sinA sinB

tan (A-B) = tanA - tan B/1+ tanA tanB

Angle Sum Identities
sin (A+B) = sinA cosB + cosA SinB

cos (A+B) = cosA cosB - sinA sinB

tan (A+B) = tanA + tan B/1-tanA tanB

Identities

Double­-Angle Identities
cos2 x = cos2 x- sin2 x

cos2 x = 2cos2 x-1

cos2 x = 1- 2sin2x

sin2 x = 2sin x cos x

tan2 x = 2tan x/1-tan2x

Half Angle Identities
sin A/2 = +/- sqrt 1-cosA/2

cos A/2 = +/- sqrt 1+cosA/2

tan A/2 = +/- sqrt 1-cosA­/1+cosA
 

Logarithms

- to base b of a positive number y is defined as...
If y=abx, then logb y= x


Log In Life
pH= -log[H+]
b is not equal to 1
b must be positive
log of 0 or negative number = undefined

log= log base 10

Log Are Inverses Of Expone­ntials

1. Graph expone­netial function
2. Graph y = x
3. Reflect expone­ntial function over y = x (reverse coodin­ates)

Properties Of Log

logb MN = logb M+ logb N <--­--p­roduct property

logb M/N= logb M - logb N <---- Quotient property

logb Mx = x logb M <--­--Power property
WATCH OUT FOR ERRORS
logb a/logb c does not equal logb a/c

logb a times c does not equal logb a times logb c

Expanding Log

log2 7b = log2 7 + log 2 b
left to right = expand

right to left = simplify

Natural Log

Write 3ln6 - ln8 as a single natural log

ln 63/8 ---> ln 216/8 ---> ln 27

Solving Log Equations

Pt 1

solve log(3x+1) = 5
3x+1 = 105
3x+1 = 100000
3x = 99,999
x = 33,333


Pt 2
Solve 2log x- log 3 = 2
log(x2/3)=2
x2/3 = 10^2
x2= 2(100)
x=10sqrt3 or 17.32

Pairs Of Relations are Inverse Of Each Other

y = x - 7/2
y = 2x+7

y = 3x - 1
y = x +1/3

y = -x + 4
y = -x + 4/-1

y = x + 4/5
y = 5x - 4
       
 

Metadata

  • Languages:
  • Published: 8th June, 2015
  • Last Updated: 12th May, 2016
  • Rated: 5 out of 5 stars based on 2 ratings

Favourited By

10noch Rxkouu nbudka40 Kristha millionanthony EzekielMamalis slabenedict

Comments

No comments yet. Add yours below!

Add a Comment

Your Comment

Please enter your name.

    Please enter your email address

      Please enter your Comment.

          Related Cheat Sheets

          Cyberlaw Final Cheat Sheet
          Exploring Knowledge First Semester 2015 Cheat Sheet
          U.S. History to 1877 Cheat Sheet