[R] stationary "terminology" time series question

[markleeds at verizon.net]

This is not exactly an R question but the R code below may make my 
question more understandable.

If one plots sin(x) where x runs from -pi to pi , then the curve hovers 
around zero obviously. so , in  a"stationary in the mean" sense,
the series is stationary. But, clearly if one plots the acf, the 
autocorrelations at lower lags are quite high and, in  the "box jenkins"
sense, this series is clearly not stationary in terms of its acf. so, 
i'm confused in terms of what ithe statistical definition of stationary 
is
as box jenkins define it ?

I don't have their text in front of me but I don't remember them having 
an example such as below when they talk about needing to difference 
series
to achieve stationarity.  thanks for any insights or a text that talks 
about this.

x <- seq(pi,-pi,by=-pi/4)
y <- sin(x)
plot(x,y)
acf(y)

P.S: this question arose because a colleague asked me to look at the 
plot of his series and the associated acf and he claims it's a 
stationary series and
I'm trying to explain to him that it is not and to try to use the acf to 
build a model for it is not reasonable.