Question

Write the method of finding an approximate value of sin(1.3) and find its value

Answer 1

How do I find the value of sin 1?

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.

Finally, you could use the Cordic Algorithm.