求函数y=√3sin2x-2sin²x 1的最小正周期
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 04:51:29
![求函数y=√3sin2x-2sin²x 1的最小正周期](/uploads/image/f/5739937-25-7.jpg?t=%E6%B1%82%E5%87%BD%E6%95%B0y%3D%E2%88%9A3sin2x-2sin%C2%B2x+1%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F)
y=sin²x+√3/2sin2x+2cos²x=√3/2sin2x+cos²x+1=√3/2sin2x+1/2(2cos²x-1)+3/2=√3/2sin2x
y=e^sin2x复合函数求导:y′=e^sin2x*cos2x*2=2cos2x*e^sin2x
y'=2cos2x
可以根据:asinα+bcosα=√(a^2+b^2)*sin(α+θ),其中θ由a,b的符号和tanθ=b/a确定具体到这题,就是:y=√[(√3+2)/2]^2+(1/2)^2*sin(2x+θ)
y=(x²+3x)^(sin2x)lny=sin2x·ln(x²+3x)y'/y=ln(x²+3x)·2cos2x+sin2x·(2x+3)/(x²+3x)y'
sin2x>0;∴0+2kπ<2x<π/2+2kπ(k∈Z)0+kπ
y=2(sinx)^2+2cosx-3=2-2(cosx)^2+2cosx-3=-2(cosx)^2+2cosx-1=-2(cosx-1/2)^2-1/2当cosx=1/2时,函数有最大值1/2,此时
y=sin2x-sin(2x-π/3)=2cos(π/3)sin2x-[sin2xcos(π/3)-cos2xsin(π/3)]=sin2xcos(π/3)+cos2xsin(π/3)=sin(2x+
令t=sinx+cosx=√sin(2x+π/4)所以t属于[-√2,√2]sin2x=2sinxcosx=(sinx+cosx)^2-1所以y=t+(t*t-1)/2+2=0.5t*t+t+1.5t
化简得:y=sin(2x+π/3)+根号3/2周期是π,增区间是(kπ-5π/12,kπ+π/12)(k属于z)
y=√3cos²x+1/2sin2x=√3/2(cos2x+1)+1/2sin2x=√3/2cos2x+1/2sin2x+√3/2=sin(π/3)cos2x+cos(π/3)sin2x+√
由y=sin2x+sin2x+3cos2x=1+sin2x+2cos2x=1+sin2x+(1+cos2x)=2sin(2x+π4)+2(1)当sin(2x+π4)=−1时,y最小=2-2,此时,由2
(1)∵y=sin2x+sin2x+3cos2x=sin2x+cos2x+2=2sin(2x+π4)+2,∴当2x+π4=2kπ-π2(k∈Z),即x=kπ-3π8(k∈Z)时,f(x)取得最小值2-
2sin2x+√3>0,且9-x^2>=0.得sin2x>-√3/2,且|x|
sin2x+1/2>0sin2x>-1/2=sin(2kπ-π/6)=sin(2kπ+7π/6)所以2kπ-π/6
sinx+cosx=√2(2/√2sinx+2/√2cos)=√2sin(x+45),令sinx+cosx=y,则y的取值[-√2,√2](sinx+cosx)^2=1+2sinxcosxsin2x=
y=[sin^2(x)+cos^2(x)]+sin(2x)+2cos^2(x)=1+sin2x+(1+cos2x)==sin2x+cos2x+2=根号(2)*sin(2x+π/4)+2当2x+π/4=
y=2sin(2x-π/3)最大值为2最小值为-2T=2π/2=π
求函数周期:Y=|sin2x|,y=|sin2x|+1/2Y=|sin2x|与y=|sin2x|+1/2的周期相同.y=sin2x与y=sin2x+1/2的最小正周期是π,那么Y=|sin2x|与y=