Категории: Все - inverse - identities - functions - trigonometry

по Cessabella Astraquillo 1 года назад

61

Trigonometry!

The study of trigonometry involves understanding various identities and functions that define the relationships between the angles and sides of triangles. Key identities include quotient identities, which express tangent and cotangent as ratios of sine and cosine, and Pythagorean identities, which relate the squares of sine, cosine, and their reciprocals.

Trigonometry!

SOH-CAH-TOA

Trigonometry!

title here

Quotient Identities

cot = cos/sin
tan = sin/cos

Basic Trigonometric Functions (super important)

Cotantgent

Abbreviation: COT


Cotangent is the reciprocal function of tangent.

Secant

Abbreviation: SEC


Secant is the reciprocal function of cosine.


(H/A)


Inverse: Arcsec or sec^-1



Cosecant

Abbreviated: CSC


Cosecant is the reciprocal of the sine function.


(H/O)


Inverse: Arccsc or csc^-1

Tangent

Abbreviated- TAN


Used to determine the ratio of a side opposite and a side adjacent of a given angle


(O/A)


Inverse: Arctan or Tan^-1

Cosine

Abbbreviated- COS


Used to determine the ratio of a side adjacent to a given angle


(A/H)


Inverse: Arccos or Cos^-1

Sine

Abbreviated: SIN


Used to determine the ratio of a side opposite of a given angle


(O/H)


Inverse: Arcsin or Sin^-1

Pythagorean Identities

1 + cot^2 = csc^2
1 + tan^2 = sec^2
sin^2 + cos^2 = 1

Even/Odd Identities

cot(-x) = -cot x
sec(-x) = -sec x
csc(-x) = -csc x
tan(-x) = -tan x
cos(-x) = -cos x
sin(-x) = -sin x

Reciprocal Identities

1/tan = cot 1/cot = tan
1/cos = sec 1/sec = cos
1/sin = csc 1/csc = sin