Introduction
 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 twodimensional triangle with one angle equal to 90 degrees). The applicability to nonrightangle triangles exists, but, since any nonrightangle triangle (on a flat plane) can be bisected to create two rightangle triangles, most problems can be reduced to calculations on rightangle triangles. Thus the majority of applications relate to rightangle triangles
What is angle
An angle which has its vertex at the origin and one side lying on the positive xaxis. 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
Degree and Radian
They both are unit of measurement of angles
Radian: A unit of measure for angles. One radian is the angle made at the centre of a circle by an arc whose length is equal to the radius of the circle.
Degree: If a rotation from the initial side to terminal side is (1/360) of a revolution, the angle is said to have a measure of one degree, written as
1°. A degree is divided into 60 minutes, and a minute is divided into 60 seconds . One sixtieth of a degree is called a minute, written as 1", and one sixtieth of a minute is called a second, written as 1'.
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 

Trigonometric Ratio's
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,Perpendicular/Hypotenuse
Trigonometric ratio's are defined as
 $\sin \theta= \frac {Perpendicular}{Hypotenuse}$
 $cosec \theta= \frac {Hypotenuse}{Perpendicular}$
 $\cos \theta= \frac {Base}{Hypotenuse}$
 $\sec \theta= \frac {Hypotenuse}{Base}$
 $\tan \theta= \frac {Perpendicular}{Base}$
 $\cot \theta= \frac {Base}{Perpendicular}$
Notice that each ratio in the righthand column is the inverse, or the reciprocal, of the ratio in the lefthand column.
The reciprocal of sin θ is csc θ ; and viceversa.
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 Trigonometric functions.
Also Read
 Notes
 Trigonometry
 Trigonometric functions
 Domain,Range And Graph of trigonometric functions
 Trigonometric Identities
 Trigonometric equations
 Values of Sin 15, cos 15 ,tan 15 ,sin 75, cos 75 ,tan 75
 values of Sin 18, cos 18, tan 18, sin 36,cos 36, Sin 54, cos 72
 Questions
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