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sine

x= length of a side opposite angle x over length of hypotenuse

Cosine

x= length of side adjacent angel x over length of hypotenuse

Tangent

x= length of side opposite angle x over length of side adjacent angel x

the cosecant

1 over sine

secant

1 over cosine

the contangent

1 over tangent

Hypotenuse

in a right triangle, the side opposite the right angle

two important coefficients

A & B

coefficients

the numbers directly in front of your variables

Amplitude

how tall it is

Period

In a large number, periods are groups of 3 digits separated by commas or by spaces.

A=1 & B=1

if there are no coefficients, then...

is it sin or cos?

first thing to check when looking at a graph

is the period changed?

2nd thing to check when looking at a graph

is the amplitude changed?

3rd things to check when looking at a graph

a sin graph..

value of 0 at 0.

a cos graph..

has a value of 1 at 0

right tri-angles

atleast 2 questions will deal with...

SOH CAH TOA

will help you remember most of the formulas

for a trig graph

focus on the amplitude and the period

the amplitude is directly related to the size of

A, while the period is inversely related to the size of B

ACT spends time reviewing..

what little content you need to ace these questions

straight forward

2 of the trig questions are..

sin

opp/hyp

cos

adj/hyp

tan

opp/adj

sine

is the opposite over hypotenuse

Cosine

is adjacent over hypotenuse

Tangent

is opposite over adjacent

the secant of any angle

is the reciprocal of the cosine

you may use Pythagorean theorem

if you have two sides of a right traignel...

Pythagorean Theorem

in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs

when a function is a whole?

you can add or subtract and also to or from the variable

when you add or subtract to or from the variable..

neither of those actions changes the shape of the graph, only its position and starting place

the amplitude

the coefficient on the outside of the functions changes..

the period

the coefficient of the inside of the functions changes

POE

process of elimination

for trig graphs..

focus on the amplitude and the period

1

cos²x+sin²x=

sec²x

1+tan²x=

csc²x

1 + cot²x

1/sin x

cscx

1/cos x

secx

sinx/cosx

tanx as two trig functions

1/tan x

cotx as one trig function

cosx/sinx

cotx as two trig functions

cscx

1/sinx

secx

1/cosx

tanx

sinx/cosx

cotx

1/tanx

cotx

cosx/sinx

y/r

what is sinθ in terms of x, y, and r

x/r

what is cosθ in terms of x, y, and r

y/x

what is tanθ in terms of x, y, and r

opp/hyp

what is sinθ in terms of sides

adj/hyp

what is cosθ in terms of sides

opp/adj

what is tanθ in terms of sides

π/180⁰

what do you multiply by to convert from degrees to radians

180⁰/π

what do you multiply by to convert from radians to degrees

1,1,√2

45⁰,45⁰,90⁰ ratio

1,√3,2

30⁰,60⁰,90⁰ ratio

30

π/6 = _______⁰

π/6

30⁰ = _______rad

60

π/3 = _______⁰

π/3

60⁰ = _______rad

45

π/4 = _______⁰

π/4

45⁰ = _______rad

90

π/2 = _______⁰

π/2

limit as x approaches ∞ of tan^-1x

cos x

cos(-x) =

-sin x

sin(-x) =

-tan x

tan(-x) =

symmetric with the y-axis

When is a function even

symmetric with the origin

When is a function odd

replace (-y) for y, yield the same equation

How do you test for symmetry with the x-axis

replace (-x) for x, yield the same equation

How do you test for symmetry with the y-axis

How do you test for symmetry with the origin

replace (-x) for x and (-y) for y, yield the same equation

opposite leg

the leg located opposite an angle of reference in a right triangle

adjacent leg

the leg located next to an angle of reference in a right triangle

opposite/hypotenuse

sine (SIN)

adjacent/hypotenuse

cosine (COS)

opposite/adjacent

tangent (TAN)

= (straight equals)

exactly equal to; answer is an integer, a simplified radical, or a number in terms of pi

(squiggle equals)

approximately equal to; answer is a decimal approximation, found by using a calculator

angle of elevation

The angle above horizontal that an observer must look to see an object that is higher than the observer. Note: The angle of elevation is congruent to the angle of depression due to the alternate interior angles theorem

angle of depression

The angle below horizontal that an observer must look to see an object that is lower than the observer. Note: The angle of depression is congruent to the angle of elevation due to the alternate interior angles theorem

Law of Sines

can be used in the cases of ASA, AAS, or SSA

Law of Cosines

can be used in the cases of SSS or SAS