Transcript A2Tslideshowreview2010x

tan  
sin 
cos 
sec 
1
cos 
csc 
1
sin 
cot  
cos 
sin 
sin   cos  
2
2
sin  
2
1  cos 
2
cos  
2
1  sin 
2
1 tan 
2
sec 
2
1 cot 
2
csc 
2
sin 2
cos 2
tan 2
Use your FORMULA
SHEET!!!!!
We use law of cosines when we have
______s.a.s._________ or
______s.s.s.____________.
r  e  g  2egCosR
2
2
2
Use law of sines when asked
to find the number of
triangles
that can be constructed.
j
a

sin J sin A
Axis of symmetry
equation: Turning point
b
x
2a
Plug in to find y!
Sum of the roots:
b

a
Product of the roots:
c
a
Quadratic formula:
b  b  4ac
x
2a
2
Use this when asked for:
a+bi, simplest radical form
or to a decimal place.
i  i
1  i
i  i
(Divide exp. By 4)
2
3
1  i
0
Completing the square:
1. Subtract/add over the constant.
2. Factor out the coefficient of the x^2
and x term, if there is one.
3. Take half of the coefficient of the x
term and square it and add it to that
side, and also add it to the other
side.
4. Factor the trinomial you made.
5. Solve for y (or x), whichever they ask
for.
ex. y  3x  12x  7
2
Discriminant is used
to determine the
types of roots:
Rational, irrational,
equal or imaginary
b  4ac
2
If:
b2  4ac  0, roots are rational and equal
b  4ac  0, imaginary roots.
2
b 2  4ac  0, roots are real, unequal and
rational (if it's a perfect square)
b  4ac  0, real, irrational, unequal (if it's
not a perfect square)
2
Conic sections:
1. circle
3. hyperbola
4. parabola
ax  ay  r
2
2
2
ax 2  by 2  c or
xy  k
2
y  ax  bx  c
Distance Formula:
d
 x1  x2    y1  y2 
2
*used to find lengths of
line segments*
2
Midpoint formula:
 x1  x2 y1  y2 
,


2 
 2
*used to find the midpoint*
y

y
1
2
Slope:
x1  x2
s r
Theta must be in radians.
Inequalities: # line, use
test points.
If <, then shade between
endpoints.
If >, then shade outside
endpoints.
To find the inverse of a
Function:
1.Switch the x and y
2.Solve for y
3. If graphing, go to table
and switch the x and y.
Inverse variation:
Multiply, do not set up a
proportion! 
Products
equal.
xy=xy
Direct variation:
x x

y y
Exponential growth and
decay.
amount after time t=initial amount(1  rate)
y  ab
Remember to change
y  a(1  r) or
t
time
x
percents by moving decimal
to the left 2 places.
Don’t forget to keep the “e”:
y  Pe
rt
This is used when there is
Continuous growth.
You can only solve
exponential equations, log
equations must be written
Exponential form first!
Find a common base or log
Both sides to solve!
log b x  p  b  x
p
Log form to:
exponent
form
log ab  log a  log b
a
log  log a  log b
b
log a  n log a
1
log x  log x
2
n
Fractional exponents:
3
2
x 
 x
3
Power over root!!!
Bottom number in the notch!
COfunctions: angles add
up to 90. complementary
sin 30 = cos 60
tan 14 = cot 76
sec 3 = csc 87
y  asinb(x  c)  d
d is the midline Vert.shift
a is the amplitude
b is the Number of
curves from 0
to 2
c is the Phase shift
2
p
b
Period is the length of one
curve.
1
arcsin x is the same as sin x
We are looking for the
angle!!, 2nd calc sin
…..etc….
Remember when solving trig
Equations, find all quadrants.
Force problems –
remember to find the
top angle.
And no, the resultant
does not bisect the angle,
only in a rhombus!!
Area of a non-right triangle
Formula sheet!!!!!
1
k  ab sin c
2
Must have 2 sides and the
Included angle!
If you see any of these, use
your FORMULA SHEET.
Binomial expansion:
st
nCr(1 term)

n r
nd
(2 term)
r
Plug in the
numbers and add
them all up!
Statistics and the Bell
Curve:
Use your formula sheet!
Mean, median, mode and
standard deviation, use
stats and 1-var stats in
your calculator.
X
For populations
Sx
For samples
If you are asked to find the
normal approximation and
not given the mean or s.d.
use these formulas and
your calculator:
mean  np and std.dev.= npq
normalcdf (low #, upper #, mean, std .dev.)
X
X
is the mean
is the population
standard deviation
S x is the sample
standard deviation
All of these are found in
1 var-stat L1,L2
when asked to graph a
complex number: a+bi,
graph it as you would the
point (a,b) and then draw
an arrow from the origin to
the point.
Ex. Find the sum of 3+4i
and -2+i, then graph the sum.
If asked to find the length
of a + bi:
a b
2
2
Y=sin x
Y=cos x
You must know the domain
and range for the inverse
trig. functions:
1
y  sin x, D : 1  x  1
R: 
1

2
y

2
y  cos x, D : 1  x  1
R: 0 y
1
y  tan x, D : all reals
R: 

2
y

2
Laws of Exponents:
x x x
a
b
ab
a
x
ab

x
b
x
a b
ab
(x )  x
1
a
x  a
x
Remember,
anything
raised to the
zero power
is one.
Fractional Exponents:
r
b b
p
p
r
Fractional Equations:
Find where denom. =0.
Multiply through by the
Least common denominator
Getting rid of the fraction.
These values go on # line!
Fractional inequalities:
You must test on the number
line and see what interval
works for your inequality.
Sequences and series:
Arithmetic – separated by a
common difference.
an  a1  (n  1)d
S
Oh yeah, it’s on
your formula sheet!
Geometric- each term is
multiplied by some number
to get to the next one. Divide
any term by the previous one
to find r, the common ratio.
an
r 
an 1
an  a1r
Sum=
n1
on your formula
sheet!
If you are given a
recursive formula, plug in
the first term to get the next
term and then plug in that
term to get the next one and
so on……… an  2an1  1
Probability:
r
C
(
p
)
(
q
)
n r
nr
At least r: r and up to n.
At most r: r and down to 0.
Probability:
Use permutations when
order is important. n
Pr
Use combinations when
order is NOT important.
C
n r
Probabilities based on
Geometric figures are the
ratio of areas.
Area formulas:
circle : a   r
rectangle: a=bh
2
Radical equations
isolate the radical
square both sides
solve for x
check your solutions
Factoring:
GCF
Difference of squares
Trinomial
By grouping
Absolute Value equations:
isolate the abs. value
set up two equations
solve for x
check your solutions
Inequalities - # line!
Functions:
Vertical line test or no
x’s repeat.
one-to-one: no x’s or
y’s repeat, horizontal
and vert. line test.
onto- all x’s and y’s
are used, a line.