已知sin(x+四分之pai)=1/3 x∈(二分之pai,pai) sinx=?

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已知sin(x+四分之pai)=1/3 x∈(二分之pai,pai) sinx=?

解;
x∈[π/2,π]
x+π/4∈[3π/4,5π/4]
∵sin(x+π/4)=1/3
∴cos(x+π/4)=-2√2/3
∴sinx
=sin(x+π/4-π/4)
=sin(x+π/4)cosπ/4-cos(x+π/4)sinπ/4
=√2/2(1/3-2√2/3)
=√2/6-2/3
=(√2-4)/6