f(a)=[sin(pai-a)cos(2pai-a)tan(-a+3pai/2)]/[cos(-pai-a)]则f(-31pai/3)=

题目

f(a)=[sin(pai-a)cos(2pai-a)tan(-a+3pai/2)]/[cos(-pai-a)]则f(-31pai/3)=

答案

诱导公式
f(a)=sinacosacota/(-cosa)
=-sinacota
=-sina(cosa/sina)
=-cosa
所以f(-31π/3)
=-cos(-31π/3)
=-cos(31π/3)
=-cos(10π+π/3)
=-cos(π/3)
=-1/2