确定下列三角函数的正负号(1)sin168°(2)cos(-600°)(3)tan(-105°)(4)sin(-17π/5)(5)cos(21π/8)(6)tan19π/5

问题描述:

确定下列三角函数的正负号
(1)sin168°
(2)cos(-600°)
(3)tan(-105°)
(4)sin(-17π/5)
(5)cos(21π/8)
(6)tan19π/5

答:
(1)sin168°=sin12°>0,正号
(2)cos(-600°)=cos600°=cos(720°-120°)=cos(-120°)=cos120°=-cos60°(3)tan(-105°)=-tan105°=-tan(180°-75°)=tan75°>0,正号
(4)sin(-17π/5)=sin(-4π+3π/5)=sin(3π/5)>0,正号
(5)cos(21π/8)=cos(2π+5π/8)=cos(5π/8)=-cos(3π/8)(6)tan(19π/5)=tan(4π-π/5)=tan(-π/5)=-tan(π/5)

sin168°为正
cos(-600°)为负
sin(-17π/5)为正
cos(21π/8)为正
tan19π/5为负

(1)sin168° 168°是第二象限角,正弦值为正(2)cos(-600°) -600°=-720°+120°,是第二象限角,余弦值为负(3)tan(-105°) -105°是第三象限角,正切值为正(4)sin(-17π/5) -17π/5=-4π+3π/5,是第二象...

正,第二象限
负,720-600=120第二象限
正,180-105=75第三象限
正,20-17=3,3π/5第二象限
负,21-16=5,5π/8第二象限
负,19-20=-1,-1/5第四象限