三角函数最值问题已知x,y,z为实数,求：f(x,y,z)=[sin(x-y)]^2+[sin(y-z)]^2+[sin

来源：学生作业帮编辑：百度作业网作业帮分类：数学作业时间：2024/07/07 07:07:32

三角函数最值问题
已知x,y,z为实数,求：f(x,y,z)=[sin(x-y)]^2+[sin(y-z)]^2+[sin(z-x)]^2的最大值.

sin^2(x-y)+sin^2(y-z)+sin^2(z-x)
=[1-cos2(x-y)+1-cos2(y-z)+1-cos2(z-x)]/2
=3/2-[(cos2xcos2y+sin2xsin2y)+(cos2ycos2z+sin2ysin2z)+(cos2zcos2x+sin2zsin2x)]/2
=3/2-[(2cos2xcos2y+2cos2ycos2z+2cos2zcos2x)+(2sin2xsin2y+2sin2ysin2z+2sin2zsin2x)+cos^2(2x)+sin^2(2x)-1+cos^2(2y)+sin^2(2y)-1+cos^2(2z)+sin^2(2z)-1]/4(这步非常关键)
=3/2-[(sin2x+sin2y+sin2z)^2+(cos2x+cos2y+cos2z)^2-3]/4
≤3/2+3/4=9/4
当x=π/3,y=2π/3,z=π时,sin2x+sin2y+sin2z)^2=(cos2x+cos2y+cos2z)^2=0
上式可以取到等号.故最大值是9/4

三角函数最值问题已知x,y,z为实数,求：f(x,y,z)=[sin(x-y)]^2+[sin(y-z)]^2+[sin 已知x,y,z都是锐角,sin^2x+sin^2y+sin^2z=1,求tanx*tany*tanz的最值证明sinx+siny+sinz-sin(x+y+z)=4sin((x+y)/2)sin((x+y)/2)sin((x+ x+y+z+sin(x+2y+3z)=0,求Zx偏导. 已知x,y,z属于(0,派/2),sin^2x+sin^2y+sin^2z=1,求(sinx+siny+sinz)/(c 三角不等式证明证明sin(x+y)+sin(y+z)+sin(z+x)>sinx+siny+sinz+sin(x+y+z 已知函数Z=F(x,y）由方程2sin（x+2y-3z)=x+2y+3z所确定,求关于x和y的偏导数求函数z=(x+y)sin(x-y)的偏导数∂z/∂x,∂z/∂y 已知x,y,z均为实数,且满足:x+2y-z=6,x-y+2z=3.求x+y+z的最小值已知x≥y≥z≥pi/12,x+y+z=pi/2,问cos x *sin y*cos z 的最大值和最小值高中必修4三角函数：①将y=sin（2x+π/4）右移z个单位（z＞0）,得到函数为偶函数,求z.②方程2sin（x+π 已知实数x,y,z满足关系式2x-3y-z=0,x-2y+z=0,求x比y比z的值