求﹙sinπ/7﹚·﹙sin2π/7﹚·﹙sin3π/7﹚的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/08 15:24:55
求﹙sinπ/7﹚·﹙sin2π/7﹚·﹙sin3π/7﹚的值

求﹙sinπ/7﹚·﹙sin2π/7﹚·﹙sin3π/7﹚的值
求﹙sinπ/7﹚·﹙sin2π/7﹚·﹙sin3π/7﹚的值

求﹙sinπ/7﹚·﹙sin2π/7﹚·﹙sin3π/7﹚的值
有一个结论
sin(π/n)*sin(2π/n)*sin(3π/n)*…*sin[(n-1)π/n] = n/ 2^(n-1)
于是
sin(π/7)*sin(2π/7)*sin(3π/7)*sin(4π/7)*sin(5π/7)*sin(6π/7) = 7/64
sin(π/7)*sin(2π/7)*sin(3π/7)*sin(3π/7)*sin(2π/7)*sin(π/7) = 7/64
sin(π/7)*sin(2π/7)*sin(3π/7) = √7 /8

一般正弦值,只有查函数表:
sinπ/7×sin2π/7×sin3π/7
=sin26°×sin52°×sin78°
=0.438×0.788×0.978
=0.338
我在网上搜的http://zhidao.baidu.com/question/59580455.html