若函数f(x)=sin2ax-sinaxcosax(a>0)的图像与直线Y=m相切,并且在Y轴右侧的切点的若函数f(x)=sin²ax-sinaxcosax(a>0)的图像与直线Y=m相切,并且在Y轴右侧的切点的横坐标依次构成公差π/2的等差数列.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/12 21:30:37
![若函数f(x)=sin2ax-sinaxcosax(a>0)的图像与直线Y=m相切,并且在Y轴右侧的切点的若函数f(x)=sin²ax-sinaxcosax(a>0)的图像与直线Y=m相切,并且在Y轴右侧的切点的横坐标依次构成公差π/2的等差数列.](/uploads/image/z/14797255-31-5.jpg?t=%E8%8B%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin2ax-sinaxcosax%28a%EF%BC%9E0%29%E7%9A%84%E5%9B%BE%E5%83%8F%E4%B8%8E%E7%9B%B4%E7%BA%BFY%3Dm%E7%9B%B8%E5%88%87%2C%E5%B9%B6%E4%B8%94%E5%9C%A8Y%E8%BD%B4%E5%8F%B3%E4%BE%A7%E7%9A%84%E5%88%87%E7%82%B9%E7%9A%84%E8%8B%A5%E5%87%BD%E6%95%B0f%28x%29%3Dsin%26sup2%3Bax-sinaxcosax%28a%EF%BC%9E0%29%E7%9A%84%E5%9B%BE%E5%83%8F%E4%B8%8E%E7%9B%B4%E7%BA%BFY%3Dm%E7%9B%B8%E5%88%87%2C%E5%B9%B6%E4%B8%94%E5%9C%A8Y%E8%BD%B4%E5%8F%B3%E4%BE%A7%E7%9A%84%E5%88%87%E7%82%B9%E7%9A%84%E6%A8%AA%E5%9D%90%E6%A0%87%E4%BE%9D%E6%AC%A1%E6%9E%84%E6%88%90%E5%85%AC%E5%B7%AE%CF%80%EF%BC%8F2%E7%9A%84%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97.)
若函数f(x)=sin2ax-sinaxcosax(a>0)的图像与直线Y=m相切,并且在Y轴右侧的切点的若函数f(x)=sin²ax-sinaxcosax(a>0)的图像与直线Y=m相切,并且在Y轴右侧的切点的横坐标依次构成公差π/2的等差数列.
若函数f(x)=sin2ax-sinaxcosax(a>0)的图像与直线Y=m相切,并且在Y轴右侧的切点的
若函数f(x)=sin²ax-sinaxcosax(a>0)的图像与直线Y=m相切,并且在Y轴右侧的切点的横坐标依次构成公差π/2的等差数列.
(1)求M的值;
(2)若点A(x0,y0)是Y=f(x)图像的对称中心,且x0∈[0,π/2],求点A的坐标.
若函数f(x)=sin2ax-sinaxcosax(a>0)的图像与直线Y=m相切,并且在Y轴右侧的切点的若函数f(x)=sin²ax-sinaxcosax(a>0)的图像与直线Y=m相切,并且在Y轴右侧的切点的横坐标依次构成公差π/2的等差数列.
做得太匆忙发现错了(鄙视抄袭的!)
(1)f(x)=(cos2αx-1)/2 -1/2(sin2αx)=1/2(cos2αx-sin2αx-1)
=-√2/2 sin(2αx+π/4)-1/2
因为与直线y=m相切,所以m等于(√2+1)/2 或 (1-√2 )/2
(2)切点的坐横标依次成公差为π/2的等差数列
说明此函数f(x)是以π/2为周期的函数
所以2π/2α = π/2 α=2 f(x)=-√2/2 sin(4x+π/4)-1/2
若点A(x0,y0)是Y=f(x)图像的对称中心,则4x+π/4=kπ
x=kπ/4-π/16 x0∈[0,π/2] 所以k=1或2
x0=3π/16或7π/16 代人A(3π/16,1/2) A(7π/16,1/2)
这回应该差不多了~