sin(－14π/3)+cos31π/6+tan(－53π/6)

题目

sin(－14π/3)+cos31π/6+tan(－53π/6)

答案

【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