设α为锐角,若cos(α+π/6)=4/5,则sin(2α+π/6)=
来源:学生作业学帮网 编辑:学帮网 时间:2024/05/17 01:01:51
设α为锐角,若cos(α+π/6)=4/5,则sin(2α+π/6)=
由cos(α+π/6)=4/5 推导出→sin(α+π/6)=3/5
引入一个sin(2α+π/3)
=sin2(α+π/6)
=2sin(α+π/6)cos(α+π/6)
=2×3/5×4/5
=24/25 推导出→cos (2α+π/3)=7/25
sin(2α+π/6)=sin[(2α+π/3)-π/6]
=sin (2α+π/3)cos π/6-cos (2α+π/3)sinπ/6
=24/25×(根号3分之2)- 7/25×2分之一
=(24根号3-7)/50
α∈(0,π/2)
α+π/6∈(π/6,2π/3)
cos(α+π/6)=4/5>0
∴α+π/6∈(π/6,π/2)
∴2α+π/3∈(π/3,π)
cos(2α+π/3)
=2cos²(α+π/6)-1
=2*(4/5)²-1
=32/25-1
=7/25>0
∴2α+π/3∈(π/3,π/2...
全部展开
α∈(0,π/2)
α+π/6∈(π/6,2π/3)
cos(α+π/6)=4/5>0
∴α+π/6∈(π/6,π/2)
∴2α+π/3∈(π/3,π)
cos(2α+π/3)
=2cos²(α+π/6)-1
=2*(4/5)²-1
=32/25-1
=7/25>0
∴2α+π/3∈(π/3,π/2)
sin(2α+π/3)=24/25
sin(2α+π/12)
=sin(2α+π/3-π/4)
=sin(2α+π/3)cosπ/4-cos(2α+π/3)sinπ/4
=24/25*√2/2-7/25*√2/2
=24√2/50-7√2/50
=17√2/50
收起
设α为锐角,若cos(α+π/6)=4/5,求sin(2α+π/12),
设α为锐角 若cos (α+π/3)=1/5则cos(α-π/6)=
设α为锐角,若cos(α+π/6)=4/5,则sin(2α+π/6)=
(江苏2012)设α为锐角,若cos(α+π/6)=4/5,则sin(2α+π/12)=
设α为锐角,若cos(α+π/6)=4/5,则sin(2α+π/12)=?
设α为锐角,若cos(α+π/3)=4/5,则sin(2α+π/6)=?
设α为锐角,若cos(α+π/6)=3/5,则sin(α-π/12)=
设α为锐角,若cos(α+π/6)=4/5,则sin(2α+π/3)的值为?
已知α为锐角,且cos(α+π/6)=4/5,则cosα
设α为锐角,tanα=3 求(cosα-sinα)/cosα+sinα)
三角函数:设a为锐角,若cos(a+π/6)=4/5,则sin(2a+π/12)的值为多少?
设a为锐角,若cos(a+π/6)=4/5,则sin(2a+π/12)的值为多少?
设a为锐角,若cos(a+π/6)=4/5,则sin(2a+π/12)值为
设a为锐角,求证 根号3/2cosa+1/2sina=cos(π/6-a) cosa-sina=根号2cos(π/4+a)
设α为锐角,求证:sinα+cosα
已知α为锐角,且cos(α+π/6)=5/13,则cosα=
设α、β均为锐角,cosα=7分之1,cos(α+β)=-4分之5,求cosβ的值如题.
若α β为锐角,sin2根号5/5,cos(a+β)=4/5,则cosβ=若αβ为锐角,sin2根号5/5,cos(a+β)=4/5,则cosβ=