Basic of Trigonometric ratios in hindi

               Trigonometry - 3

Aaj mai trigonometry ka next part  lekar aaya hu. Ab tak maine iss topic par 2 part ( part-1 aur part-2) likha hai. Agar aap part-1 aur part-2 nhi read kiya hai to maine niche diya hai . Aap read kar sakte hai.
Trigonometry part - 1
Trigonometry part - 2

Aaj mai aapko trigonometric ratio k baare me bataunga. Chaliye start karte hai. Trigonometric ratio Sabse pahle aap niche diye right angled triangle ABC ko dekhiye.

Figure-1

Uppar diye ∆ABC me aap dekh sakte hai , issk 3 sides hai -:

1. Hypotenuse
2.Opposite
3.Adjacent


1. Hypotenuse (AC) -:
Right angle triangle ABC me side AC  ko "Hypotenuse" kahate hai. Ye side , other 2 sides (AB aur BC) se badi ( big ) hoti hai. Hypotenuse (AC) ko hindi me karn (कर्ण) kahate hai. Apni suvidha k liye hum , karn ko "K" se denote karenge.

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2. Opposite (BC) -:
Side BC ko opposite side kahate hai. Humesha yaad rakhe ki , θ k saamne ( front ) wale side ko hi "opposite side" kahenge.
Jaise niche wale right angle triangle ABC k liye opposite side AB  hai. Kyuki isme θ , C par hai.

Figure-2

Iss side ko hindi me lamb (लम्ब ) kahate hai. Lamb ko hum "L" se denote karenge.

3. Adjacent (AB) -:
Figure-1 me, θ se attached wale side AB  ko "Adjacent side" kahate hai.
Figure-2 me, side BC ko "Adjacent side " kahenge.
Adjacent side ko hindi me aadhar ( आधार  ) kahate hai. Aadhar ko hum "A" se denote karenge.

Means,         L = lamb (लम्ब)
                      A = aadhar ( आधार )
                      K = karn ( कर्ण )

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Ab mai batata hu ki , trigonometric ratio kya hota hai .

What is trigonometric ratio ?

Trigonometric ratio ko hindi me " trikonmitiya anupat ( त्रिकोणमितीय  अनुपात ) kahate hai. Ab mai isska definition batata hu.

Definition of trigonometric ratio

Kisi right angled triangle k koi bhi 2 sides k ratio ko " trigonometric ratio kahate hai.

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Types of trigonometric ratio

Figure-1 se ,  Suppose karte hai ki ABC ek right angled triangle hai .
Jisme /_ABC = 90° aur  /_CAB = θ ek acute angle hai.
To isliye trigonometric ratio 6 types k hote hai -:

1. sine θ

2. cosine θ

3. tangent θ

4. cotangent θ

5. secant θ

6. cosecant θ

Aayiye ab ek- ek kark inn sabhi k baare me jaante hai.

1. sine θ -:

Opposite side AB aur Hypotenuse side BC k ratio ko sineθ kahate hai. Isse sinθ se denote karte hai.
   sinθ = opposite / hypotenuse
            = BC/AC
Hindi me ,    
                  sinθ = Lamb/karn
Or
                  sinθ = L/K   

2. cosineθ  -:

Adjacent side AB aur Hypotenuse side AC k ratio ko cosineθ kahate hai. Isse cosθ se denote karte hai.
      cosθ = Adjacent/Hypotenuse 
                = AB/AC
Hindi me ,
                   cosθ = Aadhar/karn
Or
                  cosθ = A/K


3. tangentθ -:

Opposite side BC aur Adjacent side AB k ratio ko tangentθ kahate hai. Isse tanθ se denote karte hai.
         tanθ = Opposite/Adjacent
                   = BC/AB
Hindi me ,
                   tanθ = Lamb/Aadhar
Or
                   tanθ = L/A    

4.cotangent -:

Adjacent side AB aur opposite side BC k ratio ko cotangent kahate hai. Isse cotθ se denote karte hai.
        cotθ = Adjacent/Opposite
                 = AB/BC
Hindi me ,
                  cotθ = Aadhar/Lamb
Or
                    cotθ = A/L  

5.  secantθ -:

Hypotenuse AC aur Adjacent AB k ratio ko secantθ kahate hai. Isse secθ  se denote karte hai.
       secθ = Hypotenuse/Adjacent
                 = AC/AB
Hindi me ,
                  secθ = Karn/Aadhar
Or
                   secθ = K/A       

6. cosecantθ -:

Hypotenuse AC aur Opposite AB k ratio ko cosecantθ kahte hai . Isse cosecθ se denote karte hai.
   cosecθ = Hypotenuse/Opposite
                 = AC/BC
Hindi me ,
                  cosecθ = karn/lamb
Or
                  cosecθ = K/L   

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Trigonometric ratio ko easily kaise learn kare ?

Mai aapko trigonometric ratio learn ka easy method bataunga. Jisse aapko ye sabhi ratio aashani se learn ho jaayega.

Agar aap hindi me yaad rakhna chahate hai , to aap bas niche diye formula ko yaad rakhe.

                         L A L    

                         K K A

Aap isse लाल / कक्का  k name se learn kar lijiye. Ab apko sabhi ratio yaad ho jaayenge.

Aap kahenge kaise ? Aayiye dikhata hu ,

sinθ , cosθ aur tanθ ko formula k upper likhe jaisa maine likha.
Ab up to down ⬇aap read kariye. Aap 1st 3 ratio ka formula milega.

               sinθ       cosθ       tanθ
                 L            A             L       
                 K            K             A

cosecθ , secθ aur cotθ k liye down to up ⬆aap read kare .

                 L            A             L       
                 K            K             A     
          cosecθ       secθ         cotθ



Friends , aaj k liye itana hi. apne next part-4 me iss topic se related question ko solve karna shikhenge.

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