Question

sin(a+60度)=1/3求sin(a-120度)的值

Answer 1

要求sin(a-120度)的值，首先可以用反三角函数的定义：sin(x)=1/3，即三角函数的反函数sin^-1(1/3)的值为x，即x=sin^-1(1/3)。根据三角函数的定义，sin(a+60度)=sin(a+π/3)=sin(a)+sin(π/3)=1/3。因此，a+π/3=sin^-1(1/3)，即a=sin^-1(1/3)-π/3。由于sin(a-120度)=sin((a-π/3)-π/3)=sin(a-π/3)=sin(sin^-1(1/3)-π/3-π/3)，因此sin(a-120度)=sin(-π/3)=sin(5π/3)=-1/2，所以sin(a-120度)的值为-1/2。