已知sin(a-b)=3/5 sinb=-12/13 a(π/2,π) b(-π/2,0) 求sina
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已知sin(a-b)=3/5sinb=-12/13a(π/2,π)b(-π/2,0)求sina已知sin(a-b)=3/5sinb=-12/13a(π/2,π)b(-π/2,0)求sina已知sin(
已知sin(a-b)=3/5 sinb=-12/13 a(π/2,π) b(-π/2,0) 求sina
已知sin(a-b)=3/5 sinb=-12/13 a(π/2,π) b(-π/2,0) 求sina
已知sin(a-b)=3/5 sinb=-12/13 a(π/2,π) b(-π/2,0) 求sina
a(π/2,π) b(-π/2,0)
a-b(π/2,3π/2)
又sin(a-b)=3/5
所以a-b(π/2,π)
cos(a-b)=4/5
sinb=-12/13 ,cosb=5/13
sina=sin(a-b+b)
=sin(a-b)cosb+cos(a-b)sinb
=3/5*5/13-4/5*12/13
=-33/65
bϵ(-π/2,0),aϵ(π/2,π)
-bϵ(0,π/2)
(a-b)ϵ(π/2,3π/2)
sin(a-b)=3/5>0
(a-b)ϵ(π/2,π)
cos(a-b)=-4/5
sinb=-12/13
cosb=5/13
sina=sin[(a-b)+b]=sin(a-b)cosb+ cos(a-b)sinb=63/65
a∈(π/2,π) b∈(-π/2,0),
∴a-b∈(π/2,3π/2),
cos(a-b)=-4/5,
cosb=5/13,
∴sina=sin[(a-b)+b]
=sin(a-b)cosb+cos(a-b)sinb
=3/5*5/13-4/5*(-12/13)
=(15+48)/65
=63/65.
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