用定义法,公式一以及计算器等求下列角的三个三角函数值.
3个回答
sin(2kπ+α)=sinα,cos(2kπ+α)=cosπ,tan(2kπ+α)=tanα,k∈Z
sin(π+α)=-snα,cos(π+α)=-cosα,tan(π+α)=tanα.
(1)sin(-17π/3)=sin(-6π+π/3)=sinπ/3=√3/2,
cos(-17π/3)=cosπ/3=1/2,
tan(-17π/3)=tanπ/3=√3；
(2)sin21π/4=sin[4π+(π++π/4)]=sin(π+π/4)=-sinπ/4=-√2/2,
cos21π/4=cos(π+π/4)=-cosπ/4=-√2/2,
tan21π/4=tan(π+π/4)=tanπ/4=1；
(3)sin(-23π/4)=sin(-6π+π/4)=sinπ/4=√2/2,
cos(-23π/4)=cosπ/4=√2/2,
tan(-23π/4)=tanπ/4=1；
(4)sin1500° =sin(4×360° +60° )=sin60° =√3/2,
cos1500° =cos60° =1/2,
tan1500° =tan60° =√3.
