# Sinx = x

hyurnat4
This isn't homework, rather a personal qwiggle that came up when I was in 9th grade and gone down since. The title says it all: $sin(x)=x$, solve for x. I've tried rearranging it all kinds of ways, including taylor series, but I don't seem to get anywhere. Help???

## Answers and Replies

Staff Emeritus

Try x=0, Pi, 2Pi, 3Pi, ....

Homework Helper

Draw the graph of y=x and y=sin(x) on the same coordinates and note that the gradient of sin(x) at x=0 is 1, which means that y=x is tangent to sin(x) at x=0.

Homework Helper

A typical example of what we call 'transcendental equation'. The solutions to these equations can only seldom be found exactly, in most cases only approximate numerical solutions are available. Graph intersection shows that the equation x= sin x possesses only one solution for real x and this is simply x=0. This is a very fortunate case.

hyurnat4

Thanks for that. I should have clarified: I wasn't so interested in solving for x as the maths behind it. I've never heard of these transcendental equations before. :Cue three hours of searching wikipedia and wolfram:

LawrenceC

sin(y) -> x for small y(degrees) and if x is expressed in radians. For example,
sin(.5)=.008716535. and .5/(360/2pi)=.008726646

sin(.1)=.001745328 and .1/(360/2pi)=.001745329

etc,etc

Homework Helper

sin(y) -> x for small y(degrees) and if x is expressed in radians. For example,
sin(.5)=.008716535. and .5/(360/2pi)=.008726646

sin(.1)=.001745328 and .1/(360/2pi)=.001745329

etc,etc
More simply, sin(x) is approximately equal to x for x small and in radians. I don't understand why you would want "y(degrees)". I also do not understand what this has to do with the question.

LawrenceC

....... I also do not understand what this has to do with the question.

Just some extra information for the one who posted in case he/she was not aware of it. You obviously consider it a non-sequitur. I don't.