In this paper, we study about trigonometry in finite field, we know that
, the field with
p elements, where
p is a prime number if and only if
p = 8
k + 1 or
p = 8
k -1. Let
F and
K be two fields, we say that
F is an extension of
K, if
K⊆F or there exists a monomorphism f:
K→F. Recall that
,
F[x] is the ring of polynomial over
F. If
(means that
F is an extension of
K), an element
is algebraic over
K if there exists
such that
f(u) = 0 (see [1]-[4]). The algebraic closure of
K in
F is
, which is the set of all algebraic elements in
F over
K.