Question

已知sin(a+π/4)=4/5,a∈(π/4,π/2),求sina=

已知sin(a+π/4)=4/5,a∈(π/4,π/2),求sina=已知sin(a+π/4)=4/5,a∈(π/4,π/2),求sina=

Answer 1

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解：∵a∈(π/4,π/2)
∴a+π/4∈(π/2,3π/4)
∴cos(a+π/4)<0
∴cos(a+π/4)=-√(1-(4/5)²)=-3/5
∴sina=sin[(a+π/4)-π/4]
=sin(a+π/4)cos(π/4)-sin(π/4)cos(a+π/4)
=(4/5)(√2/2)-(√2/2)(-3/5)
=7√2/10
即：sina=7√2/10
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