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Hyperbolic expressions

Inverse Hyperbolic expressions

Trigonometric functions in relation

Trigonometric meanings

sinh(x) = ( e^x - e^-x )/2... csch(x) = 1/sinh(x) = 2/( e^x - e^…

arcsinh(z) = ln( z + sqrt(z^2 + 1) )... arccosh(z) = ln( z (+-)…

sinh(z) = -i sin(iz)... csch(z) = i csc(iz)... cosh(z) = cos(iz)... se…

sin(theta) = a / c... csc(theta) = 1 / sin(theta) = c / a... cos(th…

Hyperbolic expressions

sinh(x) = ( e^x - e^-x )/2... csch(x) = 1/sinh(x) = 2/( e^x - e^…

Inverse Hyperbolic expressions

arcsinh(z) = ln( z + sqrt(z^2 + 1) )... arccosh(z) = ln( z (+-)…

Mean (Average)

Median

Mode

Probability

sum of the terms / number of terms

the middle number in a list when items are arranged in order…

the term that occurs most frequently in a list

"winning" outcomes / total possible outcomes

Mean (Average)

sum of the terms / number of terms

Median

the middle number in a list when items are arranged in order…

geometric mean

geometric mean (altitude) theorem

geometric mean (leg) theorem

for any positive numbers a and b, the positive number x such…

the altitude drawn to the hypotenuse of a right triangle sepa…

the altitude drawn to the hypotenuse of a right triangle sepa…

geometric mean

for any positive numbers a and b, the positive number x such…

geometric mean (altitude) theorem

the altitude drawn to the hypotenuse of a right triangle sepa…

Pastoral

Slaves

Had his decisions ratified by a council

Shamanism

The Mongol way of life was

Menial work in Mongol camps was done by

The Mongol leader, the khan

One religion among the serval or many that virtually all Mong…

Pastoral

The Mongol way of life was

Slaves

Menial work in Mongol camps was done by

altitude

perpendicular bisector

perpendicular lines

proportional sides

a line segment through a vertex and perpendicular to a line c…

a line which cuts a line segment into two equal parts at 90 d…

lines that intersect to form a right angle

two quantities with the same ratio

altitude

a line segment through a vertex and perpendicular to a line c…

perpendicular bisector

a line which cuts a line segment into two equal parts at 90 d…

trigonometry

sin (angle)

cos (angle)

tan (angle)

the study of the measures and relations of sides and angles i…

the value of the y where (x,y) is a point on the unit circle…

the value of the x where (x,y) is a point on the unit circle…

the calculation: y/x where (x,y) is a point on the unit circl…

trigonometry

the study of the measures and relations of sides and angles i…

sin (angle)

the value of the y where (x,y) is a point on the unit circle…

Trigonometry

Radian

Standard Position

Reference Angle

Study of sides and angles in a triangle

If arc of circle has same length as radius, than central angl…

Vertex at origin, initial ray along positive x-axis

Acute angle formed by the terminal side and nearest x-axis

Trigonometry

Study of sides and angles in a triangle

Radian

If arc of circle has same length as radius, than central angl…

logarithm

logarithmic function with base a

base of log

argument of log

inverse function (interchange the x and y)

y= loga(x) if x= a^y

a, must be greater than 0 and can't equal 1

x, what you are taking the log of, must be positive

logarithm

inverse function (interchange the x and y)

logarithmic function with base a

y= loga(x) if x= a^y

Radiance

Trigonometry

Obscuring

Pandemonium

light or heat as emitted or reflected by something

the branch of mathematics dealing with the relations of the s…

keep from being seen; conceal

wild and noisy disorder or confusion

Radiance

light or heat as emitted or reflected by something

Trigonometry

the branch of mathematics dealing with the relations of the s…

Linear

Trigonometry planar

Bent

Tetrahedral

2- bonded atoms... 0-lone pairs... 180°

3-bonded pair... 0-lone pairs... 120°

2-bonded pairs... 1 - lone pair ... 120°... Or ... 2- bonded pair... 2- lone…

4 bonded pair ... 0 lone pair... 109°

Linear

2- bonded atoms... 0-lone pairs... 180°

Trigonometry planar

3-bonded pair... 0-lone pairs... 120°

reference angle

inverse sin functions

inverse cos functions

inverse tan functions

the ACUTE angle formed by the terminal side of the angle and…

FUNCTION: y = arcsin x if and only if sin y = x... DOMAIN: -1 ≤…

FUNCTION: y = arccos x if and only if cos y = x... DOMAIN: -1 ≤…

FUNCTION: y = arctan x if and only if tan y = x... DOMAIN: -∞ ≤…

reference angle

the ACUTE angle formed by the terminal side of the angle and…

inverse sin functions

FUNCTION: y = arcsin x if and only if sin y = x... DOMAIN: -1 ≤…

Constellation

apparent magnitude

absolute magnitude

light year

1 of 88 groups or patterns of stars used to subdivide the hea…

a star's brightness compared to other stars as viewed from ea…

actual brightness of a star

the distance light travels in a year (about 9.5 trillion kilo…

Constellation

1 of 88 groups or patterns of stars used to subdivide the hea…

apparent magnitude

a star's brightness compared to other stars as viewed from ea…

Les sciences naturelles

Les mathematiques... (Les maths)

Les langues

Les sciences sociales

La biologie... La chimie... La physique

L'algebre... La geometrie... La trigonometrie... Le calcul

Le français... L'italien... L'espagnol... L'allemand... L'anglais... Le latin

L'histoire... La geographie... L'economie

Les sciences naturelles

La biologie... La chimie... La physique

Les mathematiques... (Les maths)

L'algebre... La geometrie... La trigonometrie... Le calcul

Asterism

Jonathan Bayer

A stars brightness compared to the oth…

Hipparcus

Marking with starts

Developed a way to find the stars in the sky using something…

Apparent magnitude

He invented the principles of trigonometry

Asterism

Marking with starts

Jonathan Bayer

Developed a way to find the stars in the sky using something…

Gon-

Lab-, lep-, lem-

Mes

Phra-

Angle, angled figure... Ex: Pentagon, trigonometry

To take, seize... Ex: syllable, catalepsy, dilemma

Middle... Ex: Mesopotamia, mesoderm

To speak... Ex: phrase, phraseology

Gon-

Angle, angled figure... Ex: Pentagon, trigonometry

Lab-, lep-, lem-

To take, seize... Ex: syllable, catalepsy, dilemma