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 = 8k + 1 or p = 8k -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.
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![\"\"](\"Edit_230ec271-5eef-41fd-8f4b-eede5554c2ab.png\")
, the field with p elements, where p is a prime number if and only if p = 8k + 1 or p = 8k -1. Let F and K be two fields, we say that F is an extension of K, if K![\"\"](\"Edit_a7fb39dd-d648-4b10-a115-39a10f20d624.png\")
, F[x] is the ring of polynomial over F. If ![\"\"](\"Edit_19242a3f-3c10-4c44-a0d8-234f818eb65a.bmp\")
(means that F is an extension of K), an element ![\"\"](\"Edit_0991daf0-e4c1-4ef1-9cce-144e17600065.bmp\")
is algebraic over K if there exists ![\"\"](\"Edit_d3a5212c-8da2-4aef-806b-fede1b3b70df.bmp\")
such that f(u) = 0 (see [1]-[4]). The algebraic closure of K in F is ![\"\"](\"Edit_27a33460-2987-4d17-92d1-5275ea785f6c.bmp\")
, which is the set of all algebraic elements in F over K.
