定义一种新运算,x*x=1,x*(y*z)=(x*y)z,F(X)=SINX*COS,求F(706/6)(06是派)

题目

定义一种新运算,x*x=1,x*(y*z)=(x*y)z,F(X)=SINX*COS,求F(706/6)(06是派)

答案

首先,sin(7π/6)=-1/2,cos(7π/6)=-√3/2
所以F(7π/6)=-1/2*-√3/2
而-√3/2=-1/2*√3,所以根据x*(y*z)=(x*y)*z,那么F(7π/6)=(-1/2*-1/2)*√3=1*√3