若f(n)=sin(nπ)/6,n∈N试求:f(1)*f(3)*f(5)*f(7)*…*f(101)的值
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/16 17:03:29
若f(n)=sin(nπ)/6,n∈N试求:f(1)*f(3)*f(5)*f(7)*…*f(101)的值
麻烦写上解答过程,拜托了!
麻烦写上解答过程,拜托了!
解析:∵sin(π/6)sin(3π/6)sin(5π/6)
sin(7π/6)sin(9π/6)sin(11π/6)
=sin(π/6)sin(π/2)sin(π/6)sin(-π/6)
sin(3π/2)sin(-π/6)=1/2*1*1/2*(-1/2)*(-1)*(-1/2)=-1/2^4
而sin(π/6)sin(3π/6)sin(5π/6)
sin(7π/6)sin(9π/6)sin(11π/6)
=sin(13π/6)sin(15π/6)sin(17π/6)
sin(19π/6)sin(21π/6)sin(23π/6)
=……=sin(85π/6)sin(87π/6)sin(89π/6)
sin(91π/6)sin(93π/6)sin(95π/6)
(sin(97π/6)=sin(π/6)=1/2
sin(99π/6)=sin(π/2)=1,
sin(101π/6)=sin(5π/6)=1/2
∴f(1)*f(3)*f(5)*f(7)*…*f(101)
=sin(π/6)sin(3π/6)sin(5π/6)
sin(7π/6)sin(9π/6)sin(11π/6)……sin(95π/6)sin(97π/6)sin(99π/6)sin(101π/6)
=(-1/2^4)^8*1/2*1*1/2
=1/2^32*1/4
1/2^34
sin(7π/6)sin(9π/6)sin(11π/6)
=sin(π/6)sin(π/2)sin(π/6)sin(-π/6)
sin(3π/2)sin(-π/6)=1/2*1*1/2*(-1/2)*(-1)*(-1/2)=-1/2^4
而sin(π/6)sin(3π/6)sin(5π/6)
sin(7π/6)sin(9π/6)sin(11π/6)
=sin(13π/6)sin(15π/6)sin(17π/6)
sin(19π/6)sin(21π/6)sin(23π/6)
=……=sin(85π/6)sin(87π/6)sin(89π/6)
sin(91π/6)sin(93π/6)sin(95π/6)
(sin(97π/6)=sin(π/6)=1/2
sin(99π/6)=sin(π/2)=1,
sin(101π/6)=sin(5π/6)=1/2
∴f(1)*f(3)*f(5)*f(7)*…*f(101)
=sin(π/6)sin(3π/6)sin(5π/6)
sin(7π/6)sin(9π/6)sin(11π/6)……sin(95π/6)sin(97π/6)sin(99π/6)sin(101π/6)
=(-1/2^4)^8*1/2*1*1/2
=1/2^32*1/4
1/2^34
若f(n)=sin(nπ)/6,n∈N试求:f(1)*f(3)*f(5)*f(7)*…*f(101)的值
f(n)=sin(n兀/6),求:f(1)f(3)f(5)f(7)……f(101)
已知f(n)=sin(nπ/4) (n属于整数),求f(1)×f(3)×f(5)×……×f(101)的值.
若f(n)=sin(n兀/6) 试求 f(1)+f(2)+f(3)+……f(2006) 和f(1)x f(3)xf(7)
若f(n)=sin(n兀/6) 试求 f(1)+f(2)+f(3)+……f(2008)
已知:函数f(n)=sin(nπ/6)(n属于Z),求f(1)*f(3)*f(5)*……*f(101)
已知函数f(n)=sin(nπ/6)(n为整数)求f(1)+f(2)+f(3)+...f(2013)的值
若f(n)=sinnπ6,f(1)+f(3)+f(5)+…+f(101)
已知函数f(n)=sin nπ/3(n∈Z),求f(1)+f(2)+f(3)+……+f(2013)的值和f(n)的值域
还是数学题不要忘了过程 若函数f(n)=sin nπ /6(n属于Z),则求f(1)+f(2)+f(3)+~+f(102
如果f(x)=x+1,试求f(f(f(x)))的表达式,并猜一猜f(f(f(f...f(x)...)))(n∈N+)的表
已知函数f(n)=sin[(nπ)/6],n∈Z,则f(1)+f(2)+f(3)+···+f(102)=