**Trigonometry** (from Greek *trigõnon*, "triangle" and metron, "measure") is a
branch of mathematics that studies relationships involving lengths and
angles of triangles. The field emerged during the 3^{rd} century BC from
applications of geometry to astronomical studies.

Trigonometry is most simply associated with planar right angle
triangles (each of which is a two-dimensional triangle with one angle
equal to 90 degrees). The applicability to non-right-angle triangles exists,
but, since any non-right-angle triangle (on a flat plane) can be bisected to
create two right-angle triangles, most problems can be reduced to calculations
on right-angle triangles. Thus the majority of applications relate to right-angle
triangles

An angle which has its vertex at the origin and one side lying on the positive x-axis. It can have a measure which positive or negative and can be greater than 360°

- If the direction of rotation is anticlockwise, angle is positive . If the direction of rotation is clockwise,angle is negative
- Once you have made a full circle (360°) keep going and you will see that the angle is greater than 360° .In fact you can go around as many times as you like. The same thing happens when you go clockwise. The negative angle just keeps on increasing
- It can be measured in degrees or radian

They both are unit of measurement of angles

** Radian: **A unit of measure for angles. One radian is the angle made at the
center of a circle by an arc whose length is equal to the radius of the circle.

Thus, 1° = 60', 1' = 60"

Relation between Degree and Radian

2π radian = 360 ° π radian= 180 ° 1 radian= (180/π) °

Degree | 30° | 45° | 60° | 90° | 120° | 180° | 360° |

Radian | π/6 | π/4 | π/3 | π/2 | 2π/3 | π | 2π |

In a right angle triangle ABC where B=90° ,we can define six ratio's for the two sides i.e Hypotenuse/Base, Base/Perpendicular,Perpendicular/Base,Base/hypotenuse,Hypotenuse/Perpendicular,Perpedicular/Hyptenuse
Trignometric ratio's are defined as

sin θ= Perpendicular/Hypotenuse

cosec θ= Hypotenuse/Perpendicular

cos θ= Base/Hypotenuse

sec θ= Hypotenuse/Base

tan θ= Perpendicular/Base

cot θ= Base/Perpendicular

Notice that each ratio in the right-hand column is the inverse, or the reciprocal, of the ratio in the left-hand column.

The reciprocal of sin θ is csc θ ; and vice-versa.

The reciprocal of cos θ is sec θ.

And the reciprocal of tan θ is cot θ

These are valid for acute angles.

We are now going to define them for any angles and they are called now the Trigometric functions.

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