(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 3rd
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
What is angle
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
Degree and Radian
They both are unit of measurement of angles
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.
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) °
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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