##### Triangles- revision

To understand what trygonometry is, you need to know basic informations about triangles, which you learned in geometry chapter, but to save your precious time, we prepared quick revision:

- ###### Triangle

  is a polygon with three edges and three vertices.

- ###### Right triangle

  is a triangle in which one angle is a right angle (90-degree angle).

- ###### Right triangle

  has 2 perpendicular (sides adjacent to the right angle) and 1 hypotenuse (side in opposite to right angle)

- ###### Adjacent

  is a perpendicular closer to a α angle(picture)

- ###### Opposite

  is a perpendicular further to a α angle(picture)

##### Trygonometry

Trygonometry is a branch of mathematics between angles and ratios of lengths in triangles. There are 4 trigonometric functions, such as:

Sine

###### Sine

is a trigonometric function that for an acute angle in a right triangle is the ratio of the side opposite the angle to the hypotenuse.

###### Cosine

is a trigonometric function that for an acute angle in a right triangle is the ratio of the side adjecent the angle to the hypotenuse.

###### Tangent

is a trigonometric function that is the ratio between the side opposite to an acute angle in a right triangle and the side adjecent to an acute angle.

###### Cotangent

is a trigonometric function that is the ratio between the side adjacent to an acute angle in a right triangle and the side opposite to an acute angle.

To calcualte angles in triangles using trigonometry we can use trigonometric tables:

This one is showing exact trigonometric functions values for most important angles in right traingles:

This one is showing approximate trigonometric functions values for all angles possible in right triangles:

##### Reduction formulas

What is more, it is possible to calcualte trigonometric functions values for every angle using reduction formulas, which are shown below:

sin(90∘+α)=cosα
cos(90∘+α)=−sinα
tg(90∘+α)=−ctgα
ctg(90∘+α)=−tgα
sin(90∘−α)=cosα
cos(90∘−α)=sinα
tg(90∘−α)=ctgα
ctg(90∘−α)=tgα
sin(180∘+α)=−sinα
cos(180∘+α)=−cosα
tg(180∘+α)=tgα
ctg(180∘+α)=ctgα
sin(180∘−α)=sinα
cos(180∘−α)=−cosα
tg(180∘−α)=−tgα
ctg(180∘−α)=−ctgα

sin(270∘+α)=−cosα
cos(270∘+α)=sinα
tg(270∘+α)=−ctgα
ctg(270∘+α)=−tgα
sin(270∘−α)=−cosα
cos(270∘−α)=−sinα
tg(270∘−α)=ctgα
ctg(270∘−α)=tgα
sin(360∘+α)=sinα
cos(360∘+α)=cosα
tg(360∘+α)=tgα
ctg(360∘+α)=ctgα
sin(360∘−α)=−sinα
cos(360∘−α)=cosα
tg(360∘−α)=−tgα
ctg(360∘−α)=−ctgα

##### Other formulas

During solving tasks some other formulas can come in handy, so below we put full list of them:

###### Pythagorean trigonometric identity:

###### Tangent and cotangent formulas:

###### Double-angle formulas:

###### Product identities:

###### Trigonometric addition formulas:

###### Sum identities: