Hello friend !! Aaj hum sikhenge, trigonometric ratio ki 90 degree ki value kya hoti hai? aur inn value ko nikalte kaise hai ? Means aaj hum sin90°, cos90°, tan90°, cosec90°, sec90° aur cot90° ki value jaanenge aur inn sabhi ki value nikaalna bhi sikhenge. Lekin uss se pahle hum aapko bata de ki, aaj ka lesson trigonometry part -12  hai. Toh agar aapne baaki ke sabhi part (1 to 11) nahi padhe toh humne nichey RECOMMENDED ARTICLES me diya hai. Aap chahe toh unko ek - ek karke padh sakte hai. Hume ummid hai ki, aapko jarur help milegi.

Toh ab aate hai aaj ke topic par aur aaj ka trigonometry part - 12 start karte hai. 

Trigonometric ratio 90 degree ki value kya hoti hai ? Aur inko kaise nikalte hai?

Toh jaisa ki hum upar ki line me bata chuke hai ki, aaj hum sabhi trigonometric ratio sin, cos, tan, cosec, sec aur cot ke liye 90 degree (90°) ki value (maan) nikalna sikhane waale hai. Toh isske liye hum sabse pahle ek right angle triangle lenge. Jaise niche diya huaa Figure-1 dekhiye.

Figure-1

Maan lete hai ki, upar diya Figure-1 me  ∆ABC ek samkon tribhuj (Right angle triangle) hai. Jisme ∠B = 90° ,∠A aur ∠C nyunkon (acute angle) hai. Isske saath hi ∠A ke liye side AB = aadhar (Base) aur BC = Lamb (height) hai. Iss tribhuj me sabse badi side AC = karn (hypotenuse) hai.

Ab isske baad chunki hume trigonometric ratios ki 90° ki value nikalana hai isliye hume ∆ABC me ∠A yaa ∠C dono me se kisi ek angle ko 90° banana hoga. Lekin hum ∠A ko 90° banate hai.

Right angle ∆ABC me Acute angle ∠A ko 90° kaise banaye ?

Niche diye Figure-2 me Acute angle ∠A ko 90° banane ke liye point A ko point B ki aor lekar jaana padega. Jaise jaise point A, point B ki aor jaayega vaise - vaise∠A ki value 90° ke karib hota jaayega. Means,  

               point A ➨ point B

                      ∠A ➨ 90°

figure-2

Niche diye Figure-3 se Figure-7 tak sabhi figure  me ∠A ko ∠B ki aor jaate huye dikhaya gaya hai.

figure-3

figure-4

∠A ki value jaise - jaise 90° hogi vaise - vaise ∠C chhota (small) hota jaayega. Isske saath hi side AB ki lambai (length) bhi chhoti hoti jaayegi. 

figure-6

Last me point A, point B ke bahut adhik paas aa jaata hai aur ∠A jaise hi 90° ke bahut adhik najdik hota hai toh ∠C bhi 0° ke najdik ho jaata hai. Means,  

               ∠A ➨ 90° toh

               ∠C ➨ 0°

Isske saath hi side AC, side AB ke upar aa jaati hai. Means sampaanti ho jaati hai. Nichey diya figure-7 ko dekhiye.

figure-7

Jab ∠A ka maan 90° ke bahot pass ho jaayega tab Side AB, BC aur AC ka maan kya hoga ?

Toh iss prakar se figure-7 me hum dekh sakte hai ki, Jab ∠A ka maan 90° ke bahot pass ho jaayega tab Side AB, BC aur AC ka maan ka maan bhi badal (change) jaata hai. Toh figure-2 me hum dekh sakte hai ki, ∠A = 90°, AB = 0 aur AC = BC. 

Sabhi trigonometric ratio ke liye 90° ka maan (Value)

Ab hum sabhi trigonometric ratio ki 90 degree ki value figure-7 me diye huye sabhi maano , ∠A = 90°, AB = 0 aur AC = BC  se nikalana start karte hai.

⇒ sin A = BC/AC
     sin 90° = BC/BC

                  = 1

∴ sin 90° = 1

⇒ cos A = AB/AC

     cos 90° = 0/AC

                   = 0

∴ cos 90° = 0

⇒ tan A = BC/AB

     tan 90° = BC/0

                   = undefined (aparibhasit)

∴ tan 90° = undefined

sin 90°, cos 90° aur tan 90° ki value nikalne ke baad baaki bache cosec 90°, sec 90° aur cot 90° ki value hum issi tarah se nikal sakte hai. Lekin hum cosec 90°, sec 90° aur cot 90° ki value nikalne ke liye trigonometric ratio ke reciprocal relation ka use karne jaa rahe hai-:

⇒ cosec 90° = 1/sin 90°

                       = 1/1

                       = 1

∴ cosec 90° = 1

⇒ sec 90° = 1/cos 90°

                   = 1/0

                   = undefined (aparibhasit)

∴ sec 90° = undefined

⇒ cot 90° = 1/tan 90°

                  = 1/undefined

                  = 0

∴ cot 90° = 0

Toh ab aapko sabhi trigonometric ratio ki 90° ki value maalum ho gayi hai aur inn value ko nikalne ka method bhi aap sikh chuke ho. 

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Toh friend aaj ke liye bas itna hi. Hume ummid hai ki, aapko aaj ka lesson achhe se samjh aaya hoga. Agar phir bhi aapko koi doubt yaa problem hai toh aap comment karke puchh sakte hai. Aap chahe toh apna doubt problem ki pic humare Facebook page par send kar sakte hai.

Hum aapki puri help karne ki koshish karenge. Hum issi tarah math ke ek - ek topic ko likh kar aapki mathematics ko strong karne ki koshish karte hai. Aap hume bataye ki, "Next lesson me aap kon-sa math ka topic sikhana chahte hai?"

Hum uss topic par full details me likh kar aapko samjhayenge. Toh jaldi se apna topic comment yaa massage karke bataye.

Agar aapko aaj ka lessons helpful laga ho toh please isse ek share karke humari help kariye. Thanks !