Trigonometric ratio

TRIGONOMETRY

Trigonometry  is  the  branch of  mathematics. As we know that now days it  is going to become important part of mathematics .Basically the meaning of  trigonometry is ‘Measurement of triangles’.   In Short ,we can say that Trigonometry 

ANGLE : It is formed by two lines & these line meets at common point.

MEASUREMENT OF ANGLES

There are two way by which we can measure the  angles.


     1.Sexagesimal measurement


     2.Circular measurement


Here we can see that these two methods are going to become helpful for the measurement of angles.
Now we are going to discuss sexagesimal


measurement. Now a question is arise that

What is  sexagesimal measurement?

1.sexagesimal
measurement

 When we divide a 90̊ into 90 equal parts

and divide 1̊ into 60 equal parts is called  minute (1̊= 60’).


When divide 1 minute (1’)  into 60 equal parts is called second and second is denoted as 1’=60’’.


This is the notation of angle measurement in different
form
          1 degree = 1̊
          1 minute = 1’
          1 second = 1’’
The second method, circular measurement is related to
circle.

2.circular measurement

first, we draw a circle and draw an arc PQ equal in  length of the radius.

And the center of circle is denoted as ‘O’  and take radian .

radian is denoted as 1͑.
Here π plays an important role.

Let’s define the π.
Now we can say that π is the ratio of circumference and
diameter.
π = 180̊
and the value of π is 3.14approx.


and most of the time we take 22/7 to solve the problem easily.


This is an only approximate value because π is an irrational number.


1. It is non terminating and non-repeating number.


2. It is an irrational number and comes under the real number.

3. it can be represent on a number line

Relation between radian and degree:
We have 180̊ = π


So; 1̊ = 180̊ / π ……(1)


Value of 1 / π = 0.3184


Put the value of 1 / π in equation (1)


Here we can get how many radians in 1̊.
So, 1 radian =57°16′ 

Some problems based on angle measurement.


Q. How many radians in 180̊ / π, 90̊ / π, 45̊ / π.


Sol: We have π / 180̊ degree
1̊ = π / 180̊
So, 180̊ / π = (π / 180̊ ) * (180̊ / π)
= 1 radian
Similarly;
(π / 180) * (90̊ / π)
= 1 / 2 radian
And similarly;
= (π / 180̊)*(45̊ / π)
= 1 / 4 radian

The relation between radian and degree
We have 180̊ = π
So; 1̊ = 180̊ / π ……(1)
Value of 1 / π = 0.3184
Put the value of 1 / π in equation (1)
Here we can get how many radians in 1̊.
So, 1̊ =57°16′ radian

 

There is a lot of use of trigonometry in maths.

Ex:-calculus, geometry and algebra etc.

Basically, here is the important role of angles and sides or we can say that in trigonometry we are playing with angle and sides.

In trigonometry, we are generally using some common angles like 0̊ , 30̊, 40̊, 60̊ ,90̊  etc.

Trigonometry ratios/Trigonometry functions

Trigonometry ratios are also knows as trigonometry functions. Basically three trigonometry functions are available.

Tangent, cosine and sine. these three are trigonometry ratios.

Short name of trigonometric ratios

 

  • TANGENT  (    TAN )
  • COSINE (  COS  ) 
  • SINE ( SIN )
  • Here we are taking a right angle triangle .Which have three side .The name of each side is different like hypotenuse, base and perpendicular.



  • Here trigonometry ratios;

these are basic three trigonometry functions.

NOTE:        Sinα = 1 / cosecαCosα = 1 / secαtanα = 1 / cotαNow we can say that generally six trigonometry functions are use.

 

TRIGONOMETRY ANGLE

Above ,we can see that these trigonometry angle are frequently use in trigonometry.Most of time we are using this.0̊ , 30̊, 40̊, 60̊ ,90̊ .these angles are basically use for problem .Due to this problem becomes easier.How to find the angles?

if  Sinα = P / H then

α =sin-1(P/H)similarly ,we can find the other value of angle , from this method we can find the angle.

Ex: if sinα = 1 ,find α.

Sol: As we know that

The value of ‘Sin’ is 1 at 90̊ So, α =sin-1(1)
α = 90