Question

一道高中三角函数题已知向量m=（cos x/4 ,1) 向量n=(√3sin x/4,cos^2 x/2) 若向量m*n

Answer 1

m*n=cos(x/4)*√3sin(x/4)+[cos(x/2)]^2

=(√3/2)sin(x/2)+[cos(x/2)]^2=1

(√3/2)sin(x/2)-[sin(x/2)]^2=0

[√3/2-sin(x/2)]sin(x/2)=0

sin(x/2)=√3/2或sin(x/2)=0

x/2=π/3或x/2=2π/3或x/2=π或x/2=0

x=2π/3或x=4π/3或x=0

……