已知函数f(x)=Asin(wx+φ) (A>0,w<0,-π/2<φ<π/2)一个周期的图像如图所示已知函数f(x)=Asin(wx+φ) (A>0,w<0,-π/2<φ<π/2)一个周期的图像如图所示,(1)求函数f(x)的解析式.(2)若f(a)+f(a-π/3)=24/25
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 13:07:04
![已知函数f(x)=Asin(wx+φ) (A>0,w<0,-π/2<φ<π/2)一个周期的图像如图所示已知函数f(x)=Asin(wx+φ) (A>0,w<0,-π/2<φ<π/2)一个周期的图像如图所示,(1)求函数f(x)的解析式.(2)若f(a)+f(a-π/3)=24/25](/uploads/image/z/1989571-67-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3DAsin%28wx%2B%CF%86%29+%28A%EF%BC%9E0%2Cw%EF%BC%9C0%2C-%CF%80%2F2%EF%BC%9C%CF%86%EF%BC%9C%CF%80%2F2%29%E4%B8%80%E4%B8%AA%E5%91%A8%E6%9C%9F%E7%9A%84%E5%9B%BE%E5%83%8F%E5%A6%82%E5%9B%BE%E6%89%80%E7%A4%BA%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3DAsin%28wx%2B%CF%86%29+%28A%EF%BC%9E0%2Cw%EF%BC%9C0%2C-%CF%80%2F2%EF%BC%9C%CF%86%EF%BC%9C%CF%80%2F2%29%E4%B8%80%E4%B8%AA%E5%91%A8%E6%9C%9F%E7%9A%84%E5%9B%BE%E5%83%8F%E5%A6%82%E5%9B%BE%E6%89%80%E7%A4%BA%2C%EF%BC%881%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F.%EF%BC%882%EF%BC%89%E8%8B%A5f%28a%29%2Bf%28a-%CF%80%2F3%29%3D24%2F25)
已知函数f(x)=Asin(wx+φ) (A>0,w<0,-π/2<φ<π/2)一个周期的图像如图所示已知函数f(x)=Asin(wx+φ) (A>0,w<0,-π/2<φ<π/2)一个周期的图像如图所示,(1)求函数f(x)的解析式.(2)若f(a)+f(a-π/3)=24/25
已知函数f(x)=Asin(wx+φ) (A>0,w<0,-π/2<φ<π/2)一个周期的图像如图所示
已知函数f(x)=Asin(wx+φ) (A>0,w<0,-π/2<φ<π/2)一个周期的图像如图所示,(1)求函数f(x)的解析式.(2)若f(a)+f(a-π/3)=24/25,且a为△ABC的一个内角,求sina+cosa的值
picture
已知函数f(x)=Asin(wx+φ) (A>0,w<0,-π/2<φ<π/2)一个周期的图像如图所示已知函数f(x)=Asin(wx+φ) (A>0,w<0,-π/2<φ<π/2)一个周期的图像如图所示,(1)求函数f(x)的解析式.(2)若f(a)+f(a-π/3)=24/25
(1)
从图可知:函数最大值为1,则A=1
函数f(x)的周期为T=4×(π/12+π/6)=π
而T=2π/|ω|,ω>0
∴ω=2
又x=-π/6时,y=0
∴sin[2×(-π/6)+φ]=0
而-π/2<φ<π/2
则φ=π/3
∴函数f(x)的解析式为:f(x)=sin(2x+π/3)
(2)
由f(a)+f(a-π/3)=24/25,得:
sin(2a+π/3)+sin(2a-π/3)=24/25
即2sin2acos(π/3)=24/25
∴2sinacosa=24/25
∴(sina+cosa)²=1+24/25=49/25
∵2sinacosa=24/25>0,a为△ABC的一个内角
∴sina>0,cosa>0
即sina+cosa>0
∴sina+cosa=7/5
没图怎么做啊
where the picture?