24638 cossm sm 24638 cos04964 04964 00785 find sm with c

[-2.4638 cos(sm) - sm] + [2.4638 cos(0.4964) + 0.4964] = 0.0785

find sm with complete steps?

this is a nonlinear equation in turms of sm

Solution

Given nonlinear equation:

[-2.4638 cos(sm) - sm] + [2.4638 cos(0.4964) + 0.4964] = 0.0785

Let us solve it

[-2.4638 cos(sm) - sm] + [2.4638 cos(0.4964) + 0.4964] = 0.0785

[-2.4638 cos(sm) - sm] + [2.4638 (0.9999) + 0.4964] = 0.0785

[-2.4638 cos(sm) - sm] + [2.4637 + 0.4964] = 0.0785

[-2.4638 cos(sm) - sm] + [2.9601] = 0.0785

[-2.4638 cos(sm) - sm] = 0.0785-2.9601

[-2.4638 cos(sm) - sm] = 2.8816

if we try for different values of sm,

     it satisfy for sm= - 5.3

   [-2.4638 cos(-5.3) - (-5.3)] = 2.8

    [-2.4638 (0.99) + 5.3] = 2.8

    (-2.46+5.3)=2.8

         2.8=2.8

   sm= - 5.3