tan sin

cos

sec 1

cos

csc

1

sin

cot cos

sin

2 2sin cos

2sin 21 cos

2cos 21 sin

1 tan2 sec2

1 cot2 csc2

sin 2cos2tan 2

Use your FORMULA SHEET!!!!!

We use law of cosines when we have ______s.a.s._________ or

______s.s.s.____________.

2 2 2 2r e g egCosR

Use law of sines when asked

to find the number of triangles

that can be constructed.

j

sin J

a

sin A

Axis of symmetry equation:

2

bx

a

Turning point

Plug in to find y!

Sum of the roots:

b

a

Product of the roots:

c

a

Quadratic formula:

2 4

2

b b acx

a

Use this when asked for:

a+bi, simplest radical form

or to a decimal place.

i i

1i2

i i3

1i0(Divide exp. By 4)

Completing the square:

ex. y 3x2 12x 7

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.

Discriminant is used to determine the types of roots:

Rational, irrational, equal or imaginary

2 4b ac

If:2 4 0, roots are rational and equalb ac

2 4 0, imaginary roots.b ac 2 4 0, roots are real, unequal and

rational (if it's a perfect square)

b ac

2 4 0, real, irrational, unequal (if it's

not a perfect square)

b ac

Conic sections:

1. circle 2 2 2ax ay r

3. hyperbola

ax2 by2 c or

xy k

4. parabola 2y ax bx c

Distance Formula:

2 2

1 2 1 2d x x y y

*used to find lengths of line segments*

Midpoint formula:

1 2 1 2,2 2

x x y y

*used to find the midpoint*

Slope: 1 2

1 2

y y

x x

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(1rate)time

y a(1r)t

Remember to change

percents by moving decimal

to the left 2 places.

or xy ab

Don’t forget to keep the “e”:

rty PeThis 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 pb x p b x

Log form to: exponent

form

log ab log loga b

loga

b log loga b

log na logn a1

log log2

x x

Fractional exponents:

x3

2 x 3

Power over root!!!

Bottom number in the notch!

COfunctions: angles add up to 90.

sin 30 = cos 60

tan 14 = cot 76

sec 3 = csc 87

complementary

y asinb(x c) dd is the midline

a is the amplitude

b is the Number of curves from 0 to 2

c is the Phase shift

Vert.shift

2p

b

Period is the length of one curve.

1arcsin sinx is the same as 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!!!!!

1sin

2k ab c

Must have 2 sides and the

Included angle!

If you see any of these, use your FORMULA SHEET.

Binomial expansion:

nCr(1st term)n r (2nd 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

xS 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:

and std.dev.= npq

( #, #, , . .)

mean np

normalcdf low upper mean std dev

X is the mean

X is the population standard deviation

xS 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:

2 2a b

Y=sin x

Y=cos x

You must know the domain

and range for the inverse

trig. functions:

y sin 1 x,  D :  1x 1

                   R : 2

y 2

y cos 1 x, D :  1x 1

                   R : 0 y

y tan 1 x, D : all  reals

                  R : 2

y 2

Laws of Exponents:

xa xb xab

xa

xb xa b

(xa )b xab

x a 1

xa

Remember, anything raised to the zero power is one.

Fractional Exponents:

b pr bp

r

Fractional Equations:

Multiply through by the

Least common denominator

Getting rid of the fraction.

Find where denom. =0.

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.

1

n

n

ar

a

an a1rn 1

Sum= 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……… 12 1n na a

Probability:

( ) ( )r n rn rC p q

At least r: r and up to n.

At most r: r and down to 0.

Probability:

Use permutations when

order is important.

Use combinations when

order is NOT important.

n Pr

n Cr

Probabilities based on

Geometric figures are the

ratio of areas.

Area formulas:

circle : a r2

rectangle: a=bh

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.