Jackson type theorems are established for the approximation of a function
f
f
that changes sign finitely many times in
[
−
1
,
1
]
[ - 1,1]
by polynomials
p
n
{p_n}
which are copositive with it
f
p
n
⩾
0
on
[
−
1
,
1
]
f{p_n} \geqslant 0{\text { on }}[ - 1,1]
. The results yield the rate of nonconstrained approximation and are thus best possible in the same sense as in the nonconstrained case.