Question

用公式求下列各角的三个函数值 (1)(-17π)/3 (2)(21π)/4 (3)(-23π)/6 (4)1500°

Answer 1

(1)sin(-17/3π)=sin(-17/3π+6π)
=sin(π/3)=√3/2
cos(-17/3π)=cos(π/3)=1/2
tan(-17/3π)=tan(π/3)=√3
(2)sin(21/4π)=sin(21/4π-4π)=sin(5/4π)
=sin(π+π/4)=-sinπ/4=-2√2
cos(21/4π)=cos(π+π/4)=-cosπ/4=-√2/2
tan(21/4π)=sin(21/4π)/cos(21/4π)=1
(3)sin(-23π/6)=sin(-23π/6+4π)
=sinπ/6=1/2
cos(-23π/6)=cosπ/6=√3/2
tan(-23π/6)=tanπ/6=√3
(4)sin1500°=sin(60°+1440°)=sin60°=√3/2
cos(1500°)=cos60°=1/2
tan(1500°)=tan60°=√3