1. Trigonometric functions represent elementary functions, whose argument is corner. Using trigonometric functions, the relationships between the sides and sharp corners in a right triangle. The areas of application of trigonometric functions are extremely diverse. For example, any periodic processes can be represented as a sum of trigonometric functions (Fourier series). These functions often appear when solving differential and functional equations.
2. Trigonometric functions include the following 6 functions: sinus, cosine, tangent,cotangent, secant And cosecant. For each of these functions there is an inverse trigonometric function.
3. Geometric definition trigonometric functions can be conveniently entered using unit circle. The figure below shows a circle with radius r=1. The point M(x,y) is marked on the circle. The angle between the radius vector OM and the positive direction of the Ox axis is equal to α.
4. Sinus angle α is the ratio of the ordinate y of the point M(x,y) to the radius r:
sinα=y/r.
Since r=1, then the sine is equal to the ordinate of the point M(x,y).
5. Cosine angle α is the ratio of the abscissa x of the point M(x,y) to the radius r:
cosα=x/r
6. Tangent angle α is the ratio of the ordinate y of a point M(x,y) to its abscissa x:
tanα=y/x,x≠0
7. Cotangent angle α is the ratio of the abscissa x of a point M(x,y) to its ordinate y:
cotα=x/y,y≠0
8. Secant angle α is the ratio of the radius r to the abscissa x of the point M(x,y):
secα=r/x=1/x,x≠0
9. Cosecant angle α is the ratio of the radius r to the ordinate y of the point M(x,y):
cscα=r/y=1/y,y≠0
10. In the unit circle, the projections x, y, the points M(x,y) and the radius r form a right triangle, in which x,y are the legs, and r is the hypotenuse. Therefore, the above definitions of trigonometric functions as applied to a right triangle are formulated as follows:
Sinus angle α is the ratio of the opposite side to the hypotenuse.
Cosine angle α is the ratio of the adjacent leg to the hypotenuse.
Tangent angle α is called the opposite leg to the adjacent one.
Cotangent angle α is called the adjacent side to the opposite side.
Secant angle α is the ratio of the hypotenuse to the adjacent leg.
Cosecant angle α is the ratio of the hypotenuse to the opposite leg.
11. Graph of the sine function
y=sinx, domain of definition: x∈R, range of values: −1≤sinx≤1
12. Graph of the cosine function
y=cosx, domain: x∈R, range: −1≤cosx≤1
13. Graph of the tangent function 14. Graph of the cotangent function 15. Graph of the secant function
y=tanx, range of definition: x∈R,x≠(2k+1)π/2, range of values: −∞ 
y=cotx, domain: x∈R,x≠kπ, range: −∞ 
y=secx, domain: x∈R,x≠(2k+1)π/2, range: secx∈(−∞,−1]∪∪)
