已知α属于(π/4,3π/4),β属于(0,π/4),且cos(π/4-α)=3/5,sin(5π/4+β)=-12/13求cos(α+β)

来源:学生作业帮助网 编辑:作业帮 时间:2024/04/30 06:22:28
已知α属于(π/4,3π/4),β属于(0,π/4),且cos(π/4-α)=3/5,sin(5π/4+β)=-12/13求cos(α+β)

已知α属于(π/4,3π/4),β属于(0,π/4),且cos(π/4-α)=3/5,sin(5π/4+β)=-12/13求cos(α+β)
已知α属于(π/4,3π/4),β属于(0,π/4),且cos(π/4-α)=3/5,sin(5π/4+β)=-12/13
求cos(α+β)

已知α属于(π/4,3π/4),β属于(0,π/4),且cos(π/4-α)=3/5,sin(5π/4+β)=-12/13求cos(α+β)
α∈(π/4,3π/4),
α-π/4∈(0,π/2),
cos(π/4-α)=3/5
cos(α-π/4)=3/5
sin(α-π/4)=4/5
β∈(0,π/4)
π/4+β∈(π/4,π/2)
sin(π+π/4+β)=-12/13
-sin(π/4+β)=-12/13
sin(π/4+β)=12/13
cos(π/4+β)=5/13
cos(α+β)
=cos[(α-π/4)+(π/4+β)]
=cos(α-π/4)cos(π/4+β)-sin(α-π/4)sin(π/4+β)
=3/5*5/13-4/5*12/13
=15/65-48/65
=-33/65

呼~~~好难算。。。。答案是负65分之16

已知α属于(π/4,3π/4),β属于(0,π/4),
则-α属于(-3π/4,-π/4),π/4+β属于(0,π/2),π/4-α属于(-π/2,0),
cos(π/4-α)=3/5,0>sin(π/4-α)=-√[1-cos²(π/4-α)]=-4/5,sin(5π/4+β)=-sin(π/4+β)=-12/13,
sin(π/4+β)=12/13,0

全部展开

已知α属于(π/4,3π/4),β属于(0,π/4),
则-α属于(-3π/4,-π/4),π/4+β属于(0,π/2),π/4-α属于(-π/2,0),
cos(π/4-α)=3/5,0>sin(π/4-α)=-√[1-cos²(π/4-α)]=-4/5,sin(5π/4+β)=-sin(π/4+β)=-12/13,
sin(π/4+β)=12/13,0cos(α+β)=cos[(π/4+β)-(π/4-α)]=cos(π/4+β)cos(π/4-α)]+sin(π/4+β)sin(π/4-α)
=(5/13)(3/5)+(12/13)(-4/5)=-33/65

收起

已知α属于【0,π/4】,β属于【0,π/4】且sin(2α+β)=3cos(α+β)sinα,4tanα/2=1-tan^α/2,求α+β的值 关于两角和差的余弦1.已知cosα =-12/13,cos(α+β )=17√2/26,且α属于(π,3π/2),α+β属于(3π/2,2π)求β .2.已知cos(X+Y),cos(x-y)=-4/5,x+Y属于(7π/4,2π),X-Y属于(3π/4,π)求cos2X的值.这2题自己做了,感 已知cos阿尔法=3/5,阿尔法属于(-π,0)则cos(π/4-阿尔法) 已知α属于(π/2,π),Sinα=3/5,则tan=(α-π/4)等于什么? 已知α属于(π/2,π),Sinα=3/5,则tan=(α+π/4)等于什么? 已知α属于(π/2,π),sinα=3/5,则tan(α+π/4)等于. 已知cos(π/4-α)=3/5,sin(5π/4+β)=-12/13,α属于(π/4,3π/4),β属于(0,π/4),求sin(α+β) 已知sin(α+β)=-3/5,cos(α-β)=-4/5,α+β属于(3π/2,2π),α-β属于(π/2,π),则cos2α= 已知集合A=(x x=m²-n²,m属于Z,n属于Z),求证(1)3属于A (2)偶数4k-2(k属于Z)不属于A 已知sina+cosa=3√5/5,α属于(0,π/4),sin(β-π/4)=3/5,β属于(π/4,π/2)(1)求sin2a和tan2a的值 已知a属于(0,π/4),β属于(0,π),且tan(α-β)=1/2,tanβ=-1/7,tan(2a-β)的值及角2a-β 已知sinα=3/5,cosβ=-5/13,α属于(π/2),β属于(π,3π/2),则cos(α-β)等于 已知sin(α+π/4)=12/13,a属于(π/2,π),求cos2α 已知α β 属于(0,π/2),满足tan(α+β)=4tanβ,则tanα的最大值 已知cosa=-4/5,a属于(π,3π/2)则sin(π/2)=? 已知α属于(π/2,π),sinα=3/5,则tan(α+π/4)等于 已知cosα=12/13,α属于(3π/2,2π),则cos(α+π/4)= 已知cosα=-3/5,α属于(π/2,2π)则cos(α-π/4)=