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Level 423

Trigonometry


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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