Lesson 25- Radian

 Find the circumference of a circle with radius = 1:
C= 2πr                                                                
C= 2π1
C= 2π
C= 6.3cm 
Find half a circle:
C_180®= 2 π  = πr             C₉₀= πr                    C₆₀= πr            C₄₅= πr
              2                                 2                              3                      4
Definition of Radian:
π= 3.14

Degree:	Radian:	Radian: (dec)
360°	2π	6.28
180°	π	3.14                                   -Must know!
90°	π/2	1.57                                   -Must know!
60°	π/3	1.05
45°	π/4	0.79
30°	π/5	0.57

Degrees → Radians   *find cousins
120° →  2π/ 3       150° → 5π/6     135° → 3π/ 4


1 radian → 57.3°  

Formula of Degrees → Radians or Radians→ Degrees
         π =  180
         r          d


C= Ѳr
C: arc length subtended from part circle    r: radius
Ѳ: standard angle( rads)

Lesson 24 - Trig Review

Right Triangle:

2 legs- r and q  Hyp- s
SOH- opposite over hyp.   CAH- adj. over hyp.  TOA-  opposite over adj.
 Sin R= r/s      Tan R= r/q     Cos R= q/s       Sin Q= q/s    Cos Q=r/s      Tan Q = q/r    

Non- right triangles:

Sine law Formula:             * only works with Angle Side AS triangles
Sin A   =   SinB                      

  a               b

Cosine Law Formula:   * only works with AS, Side Side

c² = a² + b²  - 2abCosC

Lesson 20 - 23

Pratice test one, two and Chapter 2 test

Lesson 19- Exponential & Log Functions

For the  equation of y= Log ₂ (2x) -2 :
Step 1-3:  Create 3 tables -  base table, inverse table and full equation table (with transformations)
Step 4: Graph table 3
Step 5: Draxy     (D: domain  R: range   A: asymtotes  X:  x-intercepts  Y:  y-intercepts)
  
Note:  Base: Log₂x   Inverse: 2 ^X    

                                                                                                 

1)      Y= 2 ^X                                             

X	Y
-2	0.25
-1	0.5
0	1
1	2
2	4

      

              2)      Y= Log₂x                                        

X	Y
0.25	-2
0.5	-1
1	0
2	1
4	2

   

    

  3)  y= Log ₂ (2x) -2
 

X	Y
0.125	-4
0.25	-3
0.5	-2
1	-1
2	0

    ←  Transformations:

     X is compressed by 1/2
     Y moved down 2

Lesson 18 - Infinite Sum & Sigma

Infinite Sum:

Formula:
S=  a   
     1- r

Example 1:
S10 = 64(1 - 0.5 ^10)     =  127.88              S20= 64(1 - 0.5 ^20)    = 127.99
                 1 - 0.5                                                          1 - 0.5

S99 = 64(1 - 0.5 ^99)    =  128                    S1000 = 64(1 - 0.5 ^1000)     = 128
                  1 - 0.5                                                             1 - 0.5

S ∞ exist only if r is a "fraction" r < 1   r > -1  r cannot = 0  

Sigma:
Formula:
  5                                      Sub 2

∑  2(-3) ^k-1                 2(-3) ^ 2-1       

k = 2                                    -6                      

5= the terms

k=2 : input term        2(-3) ^ k-1: formula

sub numbers all the way to 5  than add all numbers together or use the infinite sum formula.

Lesson 17- Geometric Sequences & Series

Geometric Sequences:

"multiplies"  ratio= r

Formula:
tn= ar^ n-1                  
r= multiplier
 tn = value   n= nth position
*note:  if you  want to find the multiplier  r= t2/a ( the 2nd number divided by the first)
Example 1:
In the following sequence: 2, 6, 18 54 .....  Find

a) t6                            b) t10          

r= 6/2=3                 = 2(3) ^ 9                
54x3= 162 t5          = 39366                     

162x 3= 484  t6                                   
                                                              
       c) which term is 9 565 938
            9565938 = 2(3)^ n-1               step1: divided by first number     
                   2                2                     step 2: log both sides  
            log 4782969 = (n-1) log3         step 3: isolate (n-1)
               log 3                      log3
                           14 = n-1                    step 4: solve
                           15 = n   
                 9565938 = t5

Series:
 A series is the sum of a sequence
S= add   t= find number

Formulas:
Sn = a(1 - r^n)         or        Sn = a- rl                            
           1 - r                                 1 - r         
  
    Sn: series ( sum)        r: ratio       l: last term> tn
    a: first #          n: how many terms there is

Example:
Find the sum of the series
5 + 15+ 45 +.......... + 885 735
Sn =  a - rl                             Sn= 5 - 3(885 735)
          1 - r                                        1 -3
                                                    =  1, 328, 600