设函数f(x)=sin2x+sintcosx+1,且f(0)9/5.(1),若t为钝角,求f(t).(2)若t为锐角且恰好等于三角形ABC的内角A,角B=30度,边长a=8,求边长b.

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设函数f(x)=sin2x+sintcosx+1,且f(0)9/5.(1),若t为钝角,求f(t).(2)若t为锐角且恰好等于三角形ABC的内角A,角B=30度,边长a=8,求边长b.
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设函数f(x)=sin2x+sintcosx+1,且f(0)9/5.(1),若t为钝角,求f(t).(2)若t为锐角且恰好等于三角形ABC的内角A,角B=30度,边长a=8,求边长b.
设函数f(x)=sin2x+sintcosx+1,且f(0)9/5.(1),若t为钝角,求f(t).(2)若t为锐角且恰好等于三角形ABC的内角A,角B=30度,边长a=8,求边长b.

设函数f(x)=sin2x+sintcosx+1,且f(0)9/5.(1),若t为钝角,求f(t).(2)若t为锐角且恰好等于三角形ABC的内角A,角B=30度,边长a=8,求边长b.
(1) f(0)=sin0+sintcos0+1=9/5
sint=4/5
∵t为钝角
∴cost=-√[1-(sint)^2]=-3/5
sin2t=2sintcost=-24/25
f(t)=sin2t+sintcost+1
=-24/25+4/5*(-3/5)+1
=-11/25
(2) b/a=sinB/sinA
b=8*sin30°/sint=8*1/2/(4/5)=5

1.f(0)=9/5代入f(x)中,得到sint=4/5
t是钝角,cost=-3/5
f(t)=sin2t+sintcost+1=3sintcost+1=-11/25
2.利用正弦公式: a/sinA=b/sinB
b=5