Question

用定义法，公式一，计算器等-17/3角的三个三角函数值

Answer 1

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。