y=-sin²x mcosX 当X∈[-π 3 2π 3] 求函数最小值

y=sin²x-1/2sinx+1=(sinx-0.25)^2+15/16当y取最大值时,sinα=-1cosα=0当y取最小值时,sinβ=1/4cosβ=正负15^0.5/4sin(α+

如果x,y都是单个元素就不用加点,如果x,y是向量或是矩阵,加点就表示相应元素进行运算,而不加点表示进行矩阵运算,当不满足维数的要求时,会出错.

x=-2:0.1:2;y=sin(x).*(x=0)+0.8*(x>0.8);plot(x,y,'*')

x=0:0.01:1;y=0;fori=1:20y=y+sin(i*x);endplot(y);

sin(x+y)sin(x-y)=-1/2(cos(x+y+x-y)—cos(x+y-x+y))=-1/2(cos2x—cos2y)=-1/2(1-2（sinx）^2-1+2(siny）^2)=（si

由函数y=sin(-2x+π/3)可知：当-2x+π/3=2kπ+π/2,k∈Z即：x=kπ-π/12,时,最大值是1；当-2x+π/3=2kπ-π/2,k∈Z即：x=kπ-5π/12,k∈Z时,最小

当x→_1__,函数y=x/x-1是无穷大,当x→__0__,函数y=x/x-1是无穷小.已知y=sin(3x),则y'=_3cos3x______

π3/4根号3-π/2--根号3

y=sin（π3+x）cos（π3-x）=（32cosx+12sinx）（12cosx+32sinx）=34+sinxcosx=34+12sin2x当函数y=sin（π3+x）cos（π3-x）取得最

当sin(x-π/3)取最小值-1时,原函数有最大值∴x-π/3=2kπ-π/2即x=2kπ-π/6,k∈Z时,函数y=1-2sin(x-π/3)取得最大值3当sin(x-π/3)取最大值1时,原函数

左边=(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)=sin²xcos²y-cos²xsin²y=sin²x(1-sin

dy/dx相当于对x进行求导：dy/dx=y'=2x*cos[sin(x^2)]*cos(x^2)由于：sinx=cosx,sin(x^2)=2x*cos(x^2)

y'sin(y/x)-y/x*sin(y/x)+1=0令y/x=u,则y'=u+xu'所以(u+xu')sinu-usinu+1=0xu'sinu+1=0-sinudu=dx/x两边积分：cosu=l

(x^x)'=(1+lnx)x^x所以y'=(1+lnx)x^xcos(x^x)

sinx+siny+sinz-sin(x+y+z)=4sin[(x+y)/2]sin[(x+z)/2]sin[(y+z)/2]sinx+siny+sinz-sin(x+y+z)=2sin[(x+y)/

lny=sinxlnx对x求导(1/y)*y'=cosx*lnx+sinx*(1/x)y'=y*[cosx*lnx+sinx*(1/x)]所以y'=x^sinx*[cosx*lnx+sinx*(1/x

-2k=cos2x-cos2y=[2(cosx)^2-1]-[2(cosy)^2-1]=2[(cosx)^2-(cosy)^2]cos^2x-cos^2y=-k

解y=sin平方x-sinx+3=sin²x-sinx+3=（sinx-1/2)²+11/4由-1≤sinx≤1即-1-1/2≤sinx-1/2≤1-1/2即-3/2≤sinx-1

利用三角形积化和差公式sin(π/3+x)cos(π-x)=sin(4π/3)-sin(-2π/3+2x)原式取得最大值时,sin(-2π/3+2x)=-1-2π/3+2x=2kπ+3/2π利用次式求

函数y=2sin(3x+π/6)当函数y取最大值时有3x+π/6=2kπ+π/2即x=2kπ/3+π/9,k∈Z所以x得集合为{x|x=2kπ/3+π/9,k∈Z}