sine function
sinθ=y/r
cosine function
cosθ=x/r
Tangent function
tanθ=y/x
Cotangent function
cotθ=x/y
secant
secθ=r/x
Csc function
csθ= r/y
(The hypotenuse is R, the opposite side is Y, and the adjacent side is X ...)
And two functions that are not commonly used and easily eliminated:
Sine and sine
Version θ
= 1-cosθ
anticosine
coversθ
= 1-sinθ
Sine: The opposite side of angle α is higher than the hypotenuse.
Cosine (cos): The adjacent side of angle α is the upper hypotenuse.
Tangent (tan): The opposite side of angle α is greater than the adjacent side.
Cotangent: The adjacent side of angle α is higher than the opposite side.
Secant: the hypotenuse of angle α is larger than the adjacent side.
Cotangent: The hypotenuse of angle α is higher than the edge.
[Edit this paragraph] The basic relationship of trigonometric functions with the same angle:
Square relation:
sin^2α+cos^2α= 1
1+tan^2α=sec^2α
1+cot^2α=csc^2α
Relationship between products:
sinα=tanα×cosα
cosα=cotα×sinα
tanα=sinα×secα
cotα= cosα×csα
secα=tanα×cscα
cscα=secα×cotα
Reciprocal relationship:
tanα
cotα= 1
sinα
cscα= 1
Coase α
secα= 1
Relationship between businesses:
sinα/cosα=tanα=secα/cscα
cosα/sinα=cotα=cscα/secα
In the right triangle ABC,
The sine value of angle a is equal to the ratio of the opposite side to the hypotenuse of angle a,
Cosine is equal to the adjacent side of angle a than the hypotenuse.
The tangent is equal to the opposite side of the adjacent side,
[1] trigonometric function identity deformation formula
Trigonometric function of sum and difference of two angles;
cos(α+β)=cosα cosβ-sinα sinβ
cos(α-β)=cosα cosβ+sinα sinβ
sin(α β)=sinα cosβ cosα sinβ
tan(α+β)=(tanα+tanβ)/( 1-tanαtanβ)
tan(α-β)=(tanα-tanβ)/( 1+tanαtanβ)
Trigonometric function of trigonometric sum:
sin(α+β+γ)= sinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγ-sinαsinβsinγ
cos(α+β+γ)= cosαcosβcosγ-cosαsinβsinγ-sinαcosβsinγ-sinαsinαsinβcosγ-sinαsinβcosγ
tan(α+β+γ)=(tanα+tanβ+tanγ-tanαtanβtanγ)/( 1-tanαtanβ-tanβtanγ-tanγtanα)
Auxiliary angle formula:
Asinα+Bcosα=(A