高中数学中经常遇到如下整数幂和问题:∑k=1nk,∑k=1nk2,∑k=1nk3,…,其中∑k=1nk可根据等差数列求和公式求得,对于∑k=1nk2,∑k=1nk3,要想直接计算难度较大.笔者结合自己的教学实际,从一组三角函数公式出发,谈谈整数幂和问题在三角函数视角下的求解.定理1 High school mathematics often encounter the following integer power and the problem: Σk = 1nk, Σk = 1nk2, Σk = 1nk3, ..., where Σk = 1nk can be obtained according to the sum of difference column summation formula for Σk = 1nk2 , Σk = 1nk3, in order to directly calculate the difficulty of the author with my teaching practice, starting from a set of trigonometric function formula, to talk about the integer power and problem solving in the perspective of trigonometric functions. Theorem 1