Question

Given that sin(45°) = 0.7071, sin(50°) = 0.7660, sin(55°) = 0.8192, sin(60°) = 0.8660. Then find sin(52°).Use Newton's forward difference formula with x = 52.​

Answer 1

Step-by-step explanation:

Given Given that sin(45°) = 0.7071, sin(50°) = 0.7660, sin(55°) = 0.8192, sin(60°) = 0.8660. Then find sin(52°).Use Newton's forward difference formula with x = 52.​

Let x be the angle and also y = f(x) = sin x

Now xo = 45 and h = 5

So x = xo + ph = 52

Now p = x – xo / h

           = 52 – 45 / 5

          = 1.4

Now we get the table as follows

So x          y              Δy                 Δ^2y                 Δ^3y

   45      0.7071      

                             0.0509

  50      0.7660                         - 0.0057

                            0.0532                                     - 0.0007

 55      0.8192                           - 0.0064

                           0.0468

60       0.8660

Now by Newton – Gregory formula we have

Y1.4 = 0.7071 + (1.4) (0.0589) + 1.4 x 0.4 / 2 (- 0.0057) + 1.4 x 0.4 x – 0.6 / 6 (- 0.0007)

        = 0.7071 + 0.08246 – 0.00160 + 0.0004

        = 0.78836

       = 0.7880 approximately

Therefore sin 52 = 0.7880

Reference link will be

https://brainly.in/question/14688434

Answer 2

Answer:

ans

ans bejo

Step-by-step explanation:

Given that sin(45°) = 0.7071, sin(50°) = 0.7660, sin(55°) = 0.8192, sin(60°) = 0.8660. Then find sin(52°).Use Newton's forward difference formula with x = 52.