cosec teta is 41/40 finnd sine teta and sec teta
Answers
Answer:
Sine theta = 40/41
Sec theta = 41/9
Step-by-step explanation:
Cosec θ = 41 / 40
Sin θ = 1 / cosec θ
Sin θ = 1 / 41 / 40
Sin θ = 40 / 41..............(1)
By using identity,
Sin ² θ + cos² θ = 1.
( 40 / 41 )² + cos² θ = 1.
cos² θ = 1 - 1600 / 1681
cos² θ = 1681 - 1600 / 1681
cos² θ = 81 / 1681
cos θ = √ 81 / 1681
Cos θ = 9 / 41................(2)
cos θ = 1 / sec θ
Sec θ = 1 / Cos θ
Sec θ = 1 / 9 / 41
Sec θ = 41 / 9
I hope you understood
Question :
If cosec∅ = 41/40 then find sin∅ and sec∅ .
Answer :
sin∅ = 40/41
sec∅ = 41/9
Note :
• sin∅ = p/h
• cos∅ = b/h
• tan∅ = p/b
• cosec∅ = 1/sin∅ = h/p
• sec∅ = 1/cos∅ = h/b
• cot∅ = 1/tan∅ = b/p
• Pythagoras theorem : In a right angled triangle , h² = p² + b²
Where ;
h = hypotenuse
p = perpendicular
b = base
Solution :
- Given : cosec∅ = 41/40
- To find : sin∅ = ? , sec∅ = ?
We have ;
cosec∅ = 41/40
Also ,
cosec∅ = h/p
Clearly ,
h = 41
p = 40
Now ,
According to the Pythagoras theorem ,
We have ;
=> h² = p² + b²
=> b² = h² - p²
=> b² = 41² - 40²
=> b² = (41 + 40)•(41 - 40)
=> b² = 81•1
=> b² = 81
=> b = √81
=> b = 9
Thus ,
sin∅ = p/h = 40/41
sec∅ = h/b = 41/9