y=sin(2x π 6) 1 2定义域怎么求
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是奇函数,还是震荡函数,函数值在[-1,1]之间震荡,在x=0处没有极限
x=0:0.01:1;y=0;fori=1:20y=y+sin(i*x);endplot(y);
因0≤x≤π/12所以π/6≤2x+π/6≤π/3则y=2sin(2x+π/6)在[0,π/12]上的最大值为2sin(π/3)=√3即y=g(x)在[0,π/12]上的最大值为√3
f(x+6π)=2sin[(x+6π)/3-π/6]=2sin(x/3+2π-π/6)=2sin(x/3-π/6)=f(x)所以6π是函数f(x)=2sin(x/3-π/6)的一个周期.
f'(x)=lim(Δx-->0)Δy/Δx=lim(Δx-->0)[sin(3x+3Δx+1)-sin(3x+1)]/Δx=lim(Δx-->0)[2cos(3x+3/2*Δx+1)sin(3Δx/
y=cos^2(3x+π/6)-sin^2(3x+π/6)=cos[2(3x+π/6)]=cos(6x+π/3)
y=sinx先向左平移π/6,得y=sin(x+π/6)然后,纵坐标不变,横坐标变为原来的1/2,得y=sin(2x+π/6)最后,向上平移3/2,得y=sin(2x+π/6)+3/2
sin(π/4+x/2)sin(π/4-x/2)=sin(π/4+x/2)sin[π/2-(π/4+x/2)]∵π/4=π/2-π/4∴sin(π/4-x/2)=sin(π/2-π/4-x)=sin[
左边=(sinxcosy+cosxsiny)(sinxcosy-cosxsiny)=sin²xcos²y-cos²xsin²y=sin²x(1-sin
∵x∈(-π/6,π); ∴2x+π/3∈(0,2π+π/3); 则函数y的最大值为1,最小值为-1; 则y∈【-1,1】
当x≥0时,sin|x/2|=sin(x/2),而sin(x/2)的最小正周期为4π;当x<0时,sin|x/2|=sin(-x/2)=-sin(x/2),-sin(x/2)的最小正周期也是4π;当-
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)/
∵0≤x≤π2,∴π6≤x+π6≤2π3;∴当x+π6=π2时,函数取得最大值是y=sin(x+π6)=1;当x+π6=π6时,函数取得最小值是y=sin(x+π6)=12;∴函数y=sin(x+π6
-2k=cos2x-cos2y=[2(cosx)^2-1]-[2(cosy)^2-1]=2[(cosx)^2-(cosy)^2]cos^2x-cos^2y=-k
f(x)=sin2(x+y/2)由于sin2x对称轴为π/4+kπ/2;故x+y/2=π/4+kπ/2x=π/4+kπ/2-y/2;将x=x=π/8代入,得y=π/4+kπ,根据y的范围可知:y=-3
令t=2x-π/12,则2x+π/6=2t+π/4,所以y=2sin(2x+π/6)+2sin(2x-π/12)=2sin(t+π/4)+2sint=√2sint+√2cost+2sint=(√2+2
对的,还可以:1.将x坐标向左平移π/6个单位2.将x坐标扩大两倍,y坐标不变
任何正弦函数,只要系数是1,值域就是[-1,1]