20: Solving for x you should get
![](gif3/ecb3cf2a.gif)
The problem now is that for a general z the expression
arccos(cos(z)) does not give z but some z0
from the basic interval of invertibility of cosine. If there is some
integer k such that
z − 2kπ
is from this basic interval, then
z0 = z − 2kπ.
In our case we have to first observe that
z = x/3 is from the interval
[5π,6π].
This means that we do not
have k as described above. The best we can do it to say that
z0 = z − 4π
lies in the basic period
of cosine, but not in its first half where we do the inverse. Thus the
expression arccos(cos(z)) doesn't really give z0
but
z1 = 2π − z0,
the picture should explain it best.
![](gif3/ecb3cf2b.gif)
Thus we get
![](gif3/ecb3cf2c.gif)
Answer