sin1° ka man nikale
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Do you have access to a scientific calculator?
sin1=0.841471
If you know the exact values of sinπ3 and π (you can get them from trigonometric tables), you can estimate sin1 using the fact that π3=1.047198≈1 .
sin1=sin[π3−(π3−1)]
⟹sin1=sinπ3cos(π3−1)−cosπ3sin(π3−1)
The angle π3−1=0.047198 is a small angle. For small angles θ , sinθ≈θ and cosθ≈1 .
sin1≈3–√2×1−12×(π3−1)
⟹sin1≈0.842427
This is correct only to two decimal places.
If not, use the Taylor Series for sinx . It converges fast enough for x=1 that you won’t lose your patience.
sinx=∑n=0∞(−1)nx2n+1(2n+1)!
Using only the first four terms gives you a value correct to four decimal places.
sin1≈1−16+1120−15040
⟹sin1≈0.841468
This is correct to four decimal places.
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