若sin(π- α)=log1/2根号2,且α属于(-2π,2),则cot(2π- α)的值
是((-2π,0),不好意思啊!写错了~不是根号3,确定是正的根号2
人气:345 ℃ 时间:2020-06-27 22:29:20
解答
α∈(-2π,0),则-α∈(0,2π)∴π- α∈(π,3π)
log1/2根号2=-log2根号2=-1/2log2(底数)2=-1/2
sin(π- α)=log1/2根号2==-1/2,π- α∈(π,3π)
π- α=7π/6或11π/6
2π- α=13π/6或17π/6
13π/6=2π+π/6,cot(2π- α)=cot(π/6)=√3
17π/6=2π-π/6,cot(2π- α)=cot(-π/6)=-cot(π/6)=-√3
所以cot(2π- α)=±√3
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