求sin(π/14)*sin(3π/14)*sin(5π/14)的值

来源:学生作业帮助网 编辑:作业帮 时间:2024/11/15 10:51:50
求sin(π/14)*sin(3π/14)*sin(5π/14)的值
x){83O|i6jyڰ&H$v6)pDXBr~D2 ," 5 5," CM§<ٱhŹ@%vFv@d;022`" 0 Ov/UU2pVC}#Z#aGŨB =ǐx~~qAb4mSVXOg3@ , X

求sin(π/14)*sin(3π/14)*sin(5π/14)的值
求sin(π/14)*sin(3π/14)*sin(5π/14)的值

求sin(π/14)*sin(3π/14)*sin(5π/14)的值
sinπ/14 sin3π/14 sin5π/14
= cos6π/14 cos4π/14 cos2π/14
=cosπ/7 cos2π/7 cos3π/7……(1)
因为2sinθcosθ=sin2θ,
又sin3π/7=sin4π/7,sin6π/7=sinπ/7
所以 (1)*sinπ/7= sinπ/7 cosπ/7 cos2π/7 cos3π/7
=1/2 sin2π/7 cos2π/7 cos3π/7
=1/4 sin4π/7 cos3π/7
=1/4 sin3π/7 cos3π/7
=1/8 sin6π/7
=1/8 sinπ/7
而(1)*sinπ/7=1/8 sinπ/7
所以(1)式=1/8

用计算器算得:0.000000901