Question

`y = sin_(fcs)(x; 1) = sin (x + sin(x + sin ( x + sin( x + ...))))`. How do you find y, at `x = 1 radian`?

Answer 1

0.93456, nearly

Explanation:

y = sin ( x + y). At, x = 1 (radian), y( 1 ) = sin ( x + 1 ). Use graphical

method or numerical iterative method for more sd in y ( 1 ).

Graphical solution y( 1 ) = 1, nearly:

graph{(y - sin ( x + y ))(x - 1 ) = 0}

Locating root for more sd, as 5-sd 0. 93456:
graph{(y - sin ( x + y ))(x - 1 ) = 0 [ 0.9999 1.0001 0.93455 0.93457]}

Note that sin ( (1 + 0.93456) radian) ) = 0.93456, nearly.

For readers interested in other FCS, some FCS generators are given

below.

#y = tan ( x + y ) = tan ( x + tan ( x + tan ( x + ...
graph{y - tan(x+y)=0}

`y = cosh( x + y ) = cosh_(fcs)( x; 1) = cosh (x + cosh (x + cosh ( x +...`
graph{y-cosh(x+y)=0}
y = `Sqrt_(fcs)( x; 1) = sqrt( x + sqrt (x + sqrt x +....`
graph{y-(x+y)^0.5 = 0}