How do you solve #x-sinx=1" and "x-sinx=-1# equations?

Question

How do you solve#x-sinx=1" and "x-sinx=-1# equations?

4280 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-26T08:16:12

No real Solutions!

From
#x-sin(x)=1# and #x-sin(x)=-1# we would get
#1=-1# which is impossible.

Answer 2 · 2018-05-26T08:55:33

The solutions are #x=1.935# and #x=-1.935#

You can solve these equations graphically

#x-sinx=1#

#<=>, #sinx=x-1#

graph{(y-sinx)(y-x+1)=0 [-7.9, 7.904, -3.95, 3.95]}

The solution is #x=1.935#

#x-sinx=-1#

#<=>, #sinx=x+1#

graph{(y-sinx)(y-x-1)=0 [-7.9, 7.904, -3.95, 3.95]}

The solution is #x=-1.935#