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what is the value of sin22.5 and how is it derived

  1. what is the value of sin22.5 and how is it derived

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2 Answers

JAGADEESH
36 Points
7 years ago
The value of Sin 22.5 is 0.382683432 .It is derived as the following
 
We know that Sin x/2 = +/-√(1-Cos x)/2
By using above formula we can derive Sin 22.5
 
Sin 22.5 = √((1−cos 45)÷2)    (Sin 22.5 is in first quadrant and Sine is positive in first quadrant,so we will use the positive square root)
 
Sin 22.5 = √((1−(1÷√2))÷2)
 
            = √((√2−1)÷(2√2))
 
          = 0.382683432
Kushagra Madhukar
askIITians Faculty 629 Points
2 years ago
Dear student,
Please find the answer to your problem.
 
We know, sin x/2 = √[(1 – cos x)/2]
or, sin 22.5o = √[(1 – cos 45o)/2]
→ sin 22.5 = √[(1 – 1/√2)/2] = 0.3827
 
Hope it helps.
Thanks and regards,
Kushagra

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