sin(-α)= sinα；

cos(-α)= cosα；

sin(π/2-α)= cosα；

cos(π/2-α)= sinα；

sin(π/2+α)= cosα；

cos(π/2+α)=-sinα；

sin(π-α)= sinα；

cos(π-α)=-cosα；

sin(π+α)=-sinα；

cos(π+α)=-cosα；

tanA = sinA/cosA；

tan(π/2+α)=-cotα；

tan(π/2-α)= cotα；

tan(π-α)=-tanα；

tan(π+α)=tanα.

The origin of trigonometric function:

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. Menelaus described Menelaus theorem of spherical surface with sine in his book "The Science of Sphere".

The application of trigonometry and astronomy in ancient Greece reached its peak in Ptolemy's time in Egypt. Ptolemy calculated the sine values of 36-degree angle and 72-degree angle in Syntaxis Mathematica, and gave the calculation methods of sum angle formula and half angle formula. Ptolemy also gave sine values corresponding to all integer radians and semi-integer radians from 0 to 180 degrees.