sin(-14π/3)+cos31π/6+tan(-53π/6)
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sin(-14π/3)+cos31π/6+tan(-53π/6)
sin(-14π/3)+cos31π/6+tan(-53π/6)
sin(-14π/3)+cos31π/6+tan(-53π/6)
【1】
sin(-14π/3)
=-sin(14π/3)
=-sin[4π+(2π/3)]
=-sin(2π/3)
=-sin[π-(π/3)]
=-sin(π/3)
=-(√3)/2
【2】
cos(31π/6)
=cos[4π+π+(π/6)]
=cos[π+(π/6)]
=-cos(π/6)
=-(√3)/2
【3】
tan(-53π/6)
=-tan[8π+π-(π/6)]
=-tan[π-(π/6)]
=tan(π/6)
=(√3)/3
【4】
原式
=(-√3)+[(√3)/3]
=(-2√3)/3
sin(-14π/3)+cos31π/6+tan(-53π/6)
=sin(-4π-2π/3)+cos(4π+7π/6)+tan(-8π-5π/6)
=sin(-2π/3)+cos(7π/6)+tan(-5π/6)
=-√3/2-√3/2+√3/3
=-2√3/3
sin(-14π/3)=sin(-14π/3+4π)=sin(-2π/3)= -sin(2π/3)=负2分之根号3
cos(31π/6)=cos(31π/6-4π)=cos(7π/6)=负2分之根号3
tan(-53π/6)=tan(-53π/6+10π)=tan7π/6=3分之根号3
sin(-14π/3)+cos31π/6+tan(-53π/6)
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