Question

Find the real root of the equation sinx=1-X using newton's raphson method​

Answer 1

Explanation:

There's no closed-form analytical solution for this kind of transcendental equation. You can either solve it graphically (as you said) or numerically. There are various methods for solving it numerically, see this Wikipedia article for an overview.

If you're not looking for a particularly efficient solution, the simplest thing to do in this case might be to write the equation as

x=1−sinx

and iterate the map

xn+1=1−sinxn

until you achieve satisfactory convergence. This is very inefficient, though; it only makes sense if you do it on a computer and don't mind if it takes a lot of operations; you'll need a lot of patience to get anywhere with it with a calculator. :-)

A far more efficient method that yields x to double-precision machine accuracy within a couple of iterations would be Newton's method:

f(x)=x+sinx−1=!0,

xn+1=xn−f(xn)f′(xn)=xn−x+sinx−11+cosx.