Trigonometry - 9
Hello friend !! Aaj hum aapko trigonometric ratios of 30 degree ke baare me batayenge. Aaj hum aapko sin 30° , cos 30° , tan 30 ° , cosec 30° , sec 30° and cot 30° ki value nikalana sikhaayenge. Inn sabhi ki value hume maalum hona jaruri hai. Hum inn sabhi value ko trigonometry se related question ko solve karne me use karenge. To chaliye aaj ka part - 9 start karte hai.
= 1/2
cos 30° = A/K = AD/AB = (x√3/2)/x
= √3/2
tan 30° = L/A = DB/AD = (x/2)/(x√3/2)
= 1/√3
Ab hume cosec 30° , sec 30° cot 30° ki value nikalna hai. Inn sabhi ki value bhi hum uppar bataye method se kar nikal sakte hai . lekin ab hum reciprocal relations ka use kark innki value nikalna bhi aapko seekhana chahte hai. To ab hum jaante hai ki ,
cosec 30 = 1/sin 30°
= 1/(1/2)
= 2
sec 30° = 1/cos 30°
= 1/(√3/2)
= 2/√3
cot 30° = 1/tan 30°
= 1/(1/√3)
= √3
To iss tarah se humne aaj aapko trigonometric ratios ke liye 30 degree ki value nikalna seekha diya.
I hope ki , aapko aaj ka trigonometric ratios of 30 degree samjh aaya hoga.
Agar aapko iss part me kisi bhi point par koi bhi problem ho rahi ho to aap hume comment karke puchh sakte hai. Hum puri koshish karenge ki aapki problem ko dur kar sake.
Humne aapki help karne ke liye iss article ko aapke saath share kiya hai aur hum chaahte hai ki iss article se unn sabhi weak students ki help ho jo math me weak hai to agar aap humari help karna chahte hai to please iss article ko share karke humari help kariye.
So friends , milte hai apne next part me. Humara ye article padane aur share karne ke liye aapka bahot - bahot shukriya.
Also read -:
• Fast multiply by 11 of any numbers in hindi
• Fast calculate square of numbers ending with 5
Hello friend !! Aaj hum aapko trigonometric ratios of 30 degree ke baare me batayenge. Aaj hum aapko sin 30° , cos 30° , tan 30 ° , cosec 30° , sec 30° and cot 30° ki value nikalana sikhaayenge. Inn sabhi ki value hume maalum hona jaruri hai. Hum inn sabhi value ko trigonometry se related question ko solve karne me use karenge. To chaliye aaj ka part - 9 start karte hai.
Trigonometric ratios of 30 degree.
Sabse pahle hum ek Equilateral triangle (sambahu tribhuj ) lenge. Iss triangle ke baare me agar aap nahi jaante to iss article triangle and its types and defination ko read kark jaan lijiye. To chaliye start karte hai.
Suppose karte hai ki , figure-1 me ∆ABC ek equilateral triangle hai. Jiski every side ki length = x aur every angle = 60° hai.
 |
| Figure-1 |
Ab hume 30 degree ki value nikalna hai isliye hum iss triangle ke kisi ek angle (60°) ko half means aadha (30°) karenge. Hum /_A ko 30° karte hai. Uske liye hum ∆ABC ke side BC ke middle me ek point D lenge. Ab point A se ek line AD , perpendicular draw karenge. (Figure-2 dekhiye.)
Tab BD = 1/2 (BC) = x/2 aur /_BAD = 30°
Ab hum dekh sakte hai ki , ∆ABD ek right angle triangle hai. Jisme angle /_D = 90° hai.
Ab ∆ADB me, /_D = 90°, karn AB = x aur BD = x/2. Iss triangle ADB me AD ki value nahi maalum hai isliye hume isski value ko nikalna padega. Iske liye hum Pythagoras theorem ka use karenge.
Isliye Pythagoras theorem se ,
AD² = AB² - BD²
= x² - (x/2)²
= x² - x²/4
= 3x²/4
⇒ AD = √(3x²/4) = x√3/2
Aapki suvidha ke liye iss right angle triangle ADB ko hum alag kar lete hai. (Figure-3 dekiye.)
/_DAB = 30° ke trigonometric ratios niche diya gaya hai:
Figure-3 me , Lamb (L) = DB , Aadhar (A) = AD aur Karn (K) = AB hai.
sin 30° = L/K = DB/AB = (x/2)/x |
| Figure-2 |
Ab hum dekh sakte hai ki , ∆ABD ek right angle triangle hai. Jisme angle /_D = 90° hai.
Ab ∆ADB me, /_D = 90°, karn AB = x aur BD = x/2. Iss triangle ADB me AD ki value nahi maalum hai isliye hume isski value ko nikalna padega. Iske liye hum Pythagoras theorem ka use karenge.
Isliye Pythagoras theorem se ,
AD² = AB² - BD²
= x² - (x/2)²
= x² - x²/4
= 3x²/4
⇒ AD = √(3x²/4) = x√3/2
Aapki suvidha ke liye iss right angle triangle ADB ko hum alag kar lete hai. (Figure-3 dekiye.)
 |
| Figure-3 |
Trigonometric ratios of 30 degree
Ab hum ek - ek karke sabhi 6 trigonometric ratios ke liye 30 degree ki value nikalna start karte hai.
Ab figure-3 se right angle ∆ADB me ,/_DAB = 30° ke trigonometric ratios niche diya gaya hai:
Figure-3 me , Lamb (L) = DB , Aadhar (A) = AD aur Karn (K) = AB hai.
= 1/2
cos 30° = A/K = AD/AB = (x√3/2)/x
= √3/2
tan 30° = L/A = DB/AD = (x/2)/(x√3/2)
= 1/√3
Ab hume cosec 30° , sec 30° cot 30° ki value nikalna hai. Inn sabhi ki value bhi hum uppar bataye method se kar nikal sakte hai . lekin ab hum reciprocal relations ka use kark innki value nikalna bhi aapko seekhana chahte hai. To ab hum jaante hai ki ,
cosec 30 = 1/sin 30°
= 1/(1/2)
= 2
sec 30° = 1/cos 30°
= 1/(√3/2)
= 2/√3
cot 30° = 1/tan 30°
= 1/(1/√3)
= √3
To iss tarah se humne aaj aapko trigonometric ratios ke liye 30 degree ki value nikalna seekha diya.
I hope ki , aapko aaj ka trigonometric ratios of 30 degree samjh aaya hoga.
Agar aapko iss part me kisi bhi point par koi bhi problem ho rahi ho to aap hume comment karke puchh sakte hai. Hum puri koshish karenge ki aapki problem ko dur kar sake.
Humne aapki help karne ke liye iss article ko aapke saath share kiya hai aur hum chaahte hai ki iss article se unn sabhi weak students ki help ho jo math me weak hai to agar aap humari help karna chahte hai to please iss article ko share karke humari help kariye.
So friends , milte hai apne next part me. Humara ye article padane aur share karne ke liye aapka bahot - bahot shukriya.
Also read -:
• Fast multiply by 11 of any numbers in hindi
• Fast calculate square of numbers ending with 5
Sir aap ye square kaise likhte hain
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