Question

已知α,β属于四分之三π,π,sin(α+β)=-五分之三,sin(β-四分之π...

已知α,β属于四分之三π,π,sin(α+β)=-五分之三,sin(β-四分之π)=十三分之十二,则cos(α+四分之π)

Answer 1

你好!
数学之美团为你解答
α,β∈(3π/4,π)
α+β∈(3π/2,2π),β
-
π/4
∈(π/2,3π/4)
sin(α+β)
=
-
3/5,sin(β
-
π/4)
=
12/13
∴cos(α+β)
=
4/5,cos(β
-
π/4)
=
-
5/13
cos(α+π/4)
=
cos
[
(α+β)
-
(β
-
π/4)
]
=
cos(α+β)cos(β
-
π/4)
+
sin(α+β)sin(β
-
π/4)
=
4/5
×
(-5/13)
+
(-3/5)
×
12/13
=
-
56/65