The relationship among tan, sin and cos is a trigonometric function, which is one of the basic elementary functions. It is a function with angle as the independent variable, and the angle corresponds to the coordinates of the intersection of the terminal edge of any angle and the unit circle or its ratio as the dependent variable.

It can also be equivalently defined as the lengths of various line segments related to the unit circle. Trigonometric function plays an important role in studying the properties of geometric shapes such as triangles and circles, and is also a basic mathematical tool for studying periodic phenomena.

sin(/2+a)= cosa；

Cos(/2+a)=- Sina; sin(2-a)= cosa； Cos(I/2-a)=sina. For triangles with side lengths of A, B and C and corresponding angles of A, B and C, there are: sinA/a=sinB/b=sinC/c, which can also be expressed as: a/sinA=b/sinB=c/sinC=2R.

It can also be expressed as: a/sinA=b/sinB=c/sinC=2R, deformation: a = 2sina, b=2RsinB, c-2RsinC. Where r is the radius of the circumscribed circle of the triangle.

In the above K/2, if k is even, the function name remains the same, and if k is odd, the function name becomes the opposite function name. The sign depends on the sign of the quadrant in the original function. There is a formula for symbols: one is all positive, the other is sine, the third is tangent, and the fourth is cosine, that is, the first quadrant is all positive, the second quadrant is sine, the third quadrant is positive, the tangent is cotangent, and the fourth quadrant is cosine.

The common * * * number (sinA)/a appearing in this theorem is the reciprocal of the diameter of a circle passing through points A, B and C..

Sine theorem is used to find unknown sides and angles when two angles and one side are known in a triangle: the problem of finding other angles and sides when the diagonal of two sides and one side is known. This is a common situation in triangulation. The sine theorem of trigonometric function can be used to find the area of triangle: s =1/2absinc =1/2bcsina =1/2acsinb.

Cosine theorem: For triangles with side lengths of A, B and C and corresponding angles of A, B and C, there are: A2 = B2+C2-2bcCOSA; B ~ 2 = A2+C ~ 2-2aCCOSB: C2 = A2+B ~ 2-2aBCOSC. This theorem can also be proved by dividing a dihedral angle into two right triangles. Cosine theorem is used to determine unknown data when two sides and an angle of a triangle are known.