First, the acute angle formula of trigonometric function:

Opposite side/hypotenuse of sinα=∞α; Adjacent side/hypotenuse of cosα=∞α; Opposite side of tanα = adjacent side of ∠ α/∠α; Adjacent side of cotα = opposite side of ∠ α/∠α.

Second, the double angle formula

Sin2A = 2SinACosAcos2a=cosa^2-sina^2= 1-2sina^2=2cosa^2- 1； Tan2a = (2 tana)/( 1-tana 2) (Note: Sina 2 is the square of Sina 2 (a))

Triple or triple angle formula

sin 3α= 4 sinαsin(π/3+α)sin(π/3-α)； cos 3α= 4 cosαcos(π/3+α)cos(π/3-α)tan3a = tana tan(π/3+a)tan(π/3-a)

Derivation of Quadruple Angle or Triple Angle Formula

sin3a = sin(2a+a)= sin 2 acosa+cos 2 asina

Fourth, the auxiliary angle formula

Asinα+bcosα = (A2+B2) (1/2) sin (α+t), where:

sint=b/(a^2+b^2)^( 1/2)； cost=a/(a^2+b^2)^( 1/2)； tant=B/A

asinα+bcosα=(a^2+b^2)^( 1/2)cos(α-t),tant=a/b

V. Power reduction formula

sin^2(α)=( 1-cos(2α))/2=versin(2α)/2

cos^2(α)=( 1+cos(2α))/2=covers(2α)/2

tan^2(α)=( 1-cos(2α))/( 1+cos(2α))

Trigonometric function ancient Greek history:

The early study of trigonometric functions can be traced back to ancient times. The founder of trigonometry in ancient Greece was Hippocius in the 2nd century BC. According to the practice of ancient Babylonians, he divided the circumference into 360 equal parts (that is, the radian of the circumference is 360 degrees, which is different from the modern arc system).

For a given radian, he gives the corresponding chord length, which is equivalent to the modern sine function. Hipachas actually given the earliest numerical table of trigonometric functions. However, trigonometry in ancient Greece was basically spherical. This is related to the fact that the main body of ancient Greek research is astronomy.

By the14th century, the Arabs' efforts to re-algebra trigonometry in arithmetic (the ancient Greeks adopted the deduction method based on geometry) laid the foundation for trigonometry to be independent from astronomy and become a more widely used discipline.