[R] plot numerous functions in one figure with different values of x per function

[Gloria_M]

To the more experienced R users,

I am not a professional programmer so please excuse me if my questions seem
naive. 
I have only begun using R to solve some problems and I'm already regretting
it

1.
I am trying to plot different functions in the same figure. The first
function 
f(x)= sin(x)+(pi/4) , -2pi<=x<=2pi
the second function
g(x) = {sin(x), 0 <= x <= pi or −2pi <= x <= -pi
         {-pi/4, elsewhere 

my code is:
> x<-seq(from=-2*pi,to=2*pi,length=1000)
> fx<- (sin(x)+(pi/4))
> plot(x,fx,type="l",lty=1)
> x2<- seq(from=0,to=pi)
> x3<- seq(from=-2*pi,to=-pi)
> gx<-(sin(x2 | x3) + (-pi/4))
> lines(x,gx,lty=2)
Error in xy.coords(x, y) : 'x' and 'y' lengths differ


it plots the first function but when I try to plot the second function it
displays the error x,y coordinates differ. I assume this is because I am
using different values for x in the first and second functions?
any ideas will be appreciated.
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