已知sin(α-π/6)=4/5,0≤α≤2π/3,求sin(5π/6-α)+cos(5π/6-α)
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/18 15:50:15
已知sin(α-π/6)=4/5,0≤α≤2π/3,求sin(5π/6-α)+cos(5π/6-α)
∵0≤α≤2π/3,∴-π/6≤α-π/6≤π/2
∵sin(α-π/6)=4/5,∴cos(α-π/6)=3/5
∴sin(α+π/6)=sin(α-π/6+π/3)
=sin(α-π/6)cosπ/3+cos(α-π/6)sinπ/3
=4/5×1/2+3/5×√3/2
=(4+3√3)/10
cos(α+π/6)=cos(α-π/6+π/3)
=cos(α-π/6)cosπ/3-sin(α-π/6)sinπ/3
=3/5×1/2-4/5×√3/2
=(3-4√3)/10
又∵sin(5π/6-α)+cos(5π/6-α)
=sin(π-(α+π/6))+cos(π-(α+π/6))
=sin(α+π/6)-cos(α+π/6)
=(4+3√3)/10-(3-4√3)/10
=(1+7√3)/10
∵sin(α-π/6)=4/5,∴cos(α-π/6)=3/5
∴sin(α+π/6)=sin(α-π/6+π/3)
=sin(α-π/6)cosπ/3+cos(α-π/6)sinπ/3
=4/5×1/2+3/5×√3/2
=(4+3√3)/10
cos(α+π/6)=cos(α-π/6+π/3)
=cos(α-π/6)cosπ/3-sin(α-π/6)sinπ/3
=3/5×1/2-4/5×√3/2
=(3-4√3)/10
又∵sin(5π/6-α)+cos(5π/6-α)
=sin(π-(α+π/6))+cos(π-(α+π/6))
=sin(α+π/6)-cos(α+π/6)
=(4+3√3)/10-(3-4√3)/10
=(1+7√3)/10
已知sin(α-π/6)=4/5,0≤α≤2π/3,求sin(5π/6-α)+cos(5π/6-α)
已知6sin²α+5sinαcosα-4cos²α=0,α∈(3π/2,2π),求tanα的值
sin²α+√3sinαcosα-2cos²α=0,α∈(π/6,5π/12),求:(1)sin(2
已知 sinα+2cos(5π/2+α)/cos(π-α)-sin(π/2-α)=-1/4 求(sinα+cosα)平方
已知6sin^2α+sinαcosα-cos^2α=0,求sin(2α+π/3)的值
已知3sinα cosα=0,求 3cosα 5sinα/sinα-cosα与sin²α 2sinα
已知sin^2α+√3sinαcosα-2cos^2a=0 α∈(π/6,5π/12)求sin(2α-π/3)和cos2
已知cos(π/2+α)=sin(α-π/2) 求sin(π-α)-cos(π+α)/cos(5π/2 -α)+2sin
已知α∈(0,π/2),且2sinα-sinαcosα-3cosα=0.求[sin(α+π/4)]/[sin2α+cos
已知α∈(π,2π) sinα+cosα=1/5 求sinα*cosα sinα-cosα
已知sin(α-β)cosα-cos(β-α)sinα=3/5,β是第三象限角,求sin(β+5π/4)的值
化简:1、sin(x-π/3)-cos(x+π/6)+√3cosx=?2、已知,sinα+sinβ=√2/2,求cosα