Solve for x, x-sinex=0... where x is not equal to zero?

Question

thanks in advance..

Answer 1

Subtract x from each side,

x = sin x

For trig, x is in natural units (radians). Since -1≤ sin x ≤ 1, only values for x between -1 and 1 need be checked.

Sin is determined numerically. Exploring it in Excel, there are no values that meet the requirements except x=0.

Now, d/dx sin x = cos x.

This means that sin x at zero starts out changing at the same rate as x at x=0 (since cos 0 = 1). But it falls off as x gets away from zero, and the greater is gets, the more it falls off. Performance for x<0 is the same. Thus, no roots other than zero.