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因为:θ∈(π/2,π),
所以:θ-π/4∈(π/4,3π/4)
因此:sin(θ-π/4)>0
又:cos(θ-π/4)=3/5
而:sin²(θ-π/4)+cos²(θ-π/4)=1
所以,sin²(θ-π/4)=1-cos²(θ-π/4)=1-(3/5)²=16/25
由此得:sin(θ-π/4)=4/5
cosθ=cos[(θ-π/4)+π/4]
=cos(θ-π/4)cos(π/4)-sin(θ-π/4)sin(π/4)
=(3/5)(√2)/2-(4/5)(√2)/2
=(3/10)√2-(4/10)√2
=-(√2)/10
1年前
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