给出下列命题:(1)函数f(x)=4sin(2x+π/3)的图像关于点(-π/6,0)对称(2)函数g(x)=-3sin(2x-π/3)在区间(-π/12,5π/12)内时增函数(3)函数h(x)=sin(2/3x-7π/2)是偶函数(4)存在实数x,使sinx+cosx
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/23 19:20:19
![给出下列命题:(1)函数f(x)=4sin(2x+π/3)的图像关于点(-π/6,0)对称(2)函数g(x)=-3sin(2x-π/3)在区间(-π/12,5π/12)内时增函数(3)函数h(x)=sin(2/3x-7π/2)是偶函数(4)存在实数x,使sinx+cosx](/uploads/image/z/3577725-45-5.jpg?t=%E7%BB%99%E5%87%BA%E4%B8%8B%E5%88%97%E5%91%BD%E9%A2%98%EF%BC%9A%EF%BC%881%EF%BC%89%E5%87%BD%E6%95%B0f%28x%29%3D4sin%282x%2B%CF%80%2F3%29%E7%9A%84%E5%9B%BE%E5%83%8F%E5%85%B3%E4%BA%8E%E7%82%B9%28-%CF%80%2F6%2C0%29%E5%AF%B9%E7%A7%B0%EF%BC%882%EF%BC%89%E5%87%BD%E6%95%B0g%28x%29%3D-3sin%EF%BC%882x-%CF%80%2F3%EF%BC%89%E5%9C%A8%E5%8C%BA%E9%97%B4%EF%BC%88-%CF%80%2F12%2C5%CF%80%2F12%EF%BC%89%E5%86%85%E6%97%B6%E5%A2%9E%E5%87%BD%E6%95%B0%EF%BC%883%EF%BC%89%E5%87%BD%E6%95%B0h%EF%BC%88x%EF%BC%89%3Dsin%EF%BC%882%2F3x-7%CF%80%2F2%EF%BC%89%E6%98%AF%E5%81%B6%E5%87%BD%E6%95%B0%EF%BC%884%EF%BC%89%E5%AD%98%E5%9C%A8%E5%AE%9E%E6%95%B0x%2C%E4%BD%BFsinx%2Bcosx)
给出下列命题:(1)函数f(x)=4sin(2x+π/3)的图像关于点(-π/6,0)对称(2)函数g(x)=-3sin(2x-π/3)在区间(-π/12,5π/12)内时增函数(3)函数h(x)=sin(2/3x-7π/2)是偶函数(4)存在实数x,使sinx+cosx
给出下列命题:(1)函数f(x)=4sin(2x+π/3)的图像关于点(-π/6,0)对称(2)函数g(x)=-3sin(2x-π/3)在区间(-π/12,5π/12)内时增函数(3)函数h(x)=sin(2/3x-7π/2)是偶函数(4)存在实数x,使sinx+cosx=π/3
其中正确的序号是?
给出下列命题:(1)函数f(x)=4sin(2x+π/3)的图像关于点(-π/6,0)对称(2)函数g(x)=-3sin(2x-π/3)在区间(-π/12,5π/12)内时增函数(3)函数h(x)=sin(2/3x-7π/2)是偶函数(4)存在实数x,使sinx+cosx
1.函数f(x)=4sin(2x+π/3)的图像关于点(-π/6,0)对称
将x=-π/6代入,f(-π/6)=4sin(-π/3+π/3)=0
∴1是真命题
2.函数g(x)=-3sin(2x+π/3)在区间(-π/12,5π/12)内时增函数
x∈(-π/12,5π/12),2x∈(-π/6,5π/6),2x+π/3 ∈(π/6,7π/6)
2是假命题
3.函数h(x)=sin(2/3x-7π/2)是偶函数
h(x)=sin(2/3x+π/2)=cos2/3x 是偶函数,真命题
4.存在实数使sinx+cosx=π/3
sinx+cosx=√2sin(x+π/4)∈[-√2,√2],π/3)∈[-√2,√2] 真命题
∴其中正确的有1,3,4