Alrighty so last week we finished taking our chapter tests. I think this week is ACT prep so hopefully we review ACT stuff in math. I am going to review some trig from Ch. 10.
Law of Sines:
sinA/a = sinB/b = sinC/c
Law of Cosines:
(opp leg)^2 = (adj leg)^2 + (other adj leg)^2 -2(adj leg)(adj leg)cos(angle between)
Example:
x= 6^2 + 5^2 -2(5)(6) cos 36
x=3.530
Here are some formulas:
Cos(α +/- β)=cos α cos β -/+ sin α sin β
sin(α +/- β)=sin α cos β -/+ cos α sin β
sin x + sin y= 2 sin x + y/2 cos x-y/2
sin x - sin y= 2 cos x + y/2 sin x-y/2
cos x + cos y= 2 cos x + y/2 cos x-y/2
cos x - cos y= 2 sin x + y/2 sin x-y/2
tan (α + β)=tan α + tan β/1-tan α tan β
tan (α - β)=tan α - tan β/1+tan α tan β
sin2α=2sin α cos α
cos 2α=cos^2 α –sin^2 α = 1-2 sin^2 α= 2 cos^2 α -1
tan 2α = 2tan α /1-tan^2 α
sin α/2= +/- √1-cos α/2
cos α/2= +/- √1+ cos α/2
tan α/2= +/- √1-cos α or 1 + cos α
=sin α/1+cos α
=1-cos α/sin α
I could use some help with sigma notation
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Sigma has three parts
ReplyDeleteA top number
A middle number
A bottom number
Top is called limit of summation
Middle is called the summand
Bottom is called index
Top is the address of the last number in given series
Middle is the result of the tn formula
Bottom is what number you start counting at
If the equation is arithmetic then the bottom number will be 1
If the equation is geometric then the bottom number will be 0
When asked to evaluate for a sigma problem you plug in the numbers including and between the bottom and the top numbers
So if the bottom number is one and the top number is five then you would plug in 1,2,3,4,5 for the variable of the middle equation and add the results of each plug in togethe3r to get the final answer
When asked to express then you draw the sigma sign and fill in the top middle and bottom parts