已知函数f(x)=sin(2x-A)+1满足f((π/3)+x)=f((π/3)-x),则A等于多少?
来源:学生作业帮 编辑:百度作业网作业帮 分类:综合作业 时间:2024/08/19 17:28:02
已知函数f(x)=sin(2x-A)+1满足f((π/3)+x)=f((π/3)-x),则A等于多少?
![已知函数f(x)=sin(2x-A)+1满足f((π/3)+x)=f((π/3)-x),则A等于多少?](/uploads/image/z/1305170-26-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dsin%EF%BC%882x-A%EF%BC%89%2B1%E6%BB%A1%E8%B6%B3f%EF%BC%88%EF%BC%88%CF%80%2F3%EF%BC%89%2Bx%29%3Df%EF%BC%88%EF%BC%88%CF%80%2F3%EF%BC%89-x%29%2C%E5%88%99A%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
令x=π/3 代入f((π/3)+x)=f((π/3)-x)
f(0)=sinA+1=f(2π/3)=sin((4π/3)-A)+1
sinA=sin((4π/3)-A)=sin(4π/3)cosA-cos(4π/3)sinA/2((1-sinA)^0.5=-3^0.5/2((1-(sinA)^2)^0.5)+0.5sinA
移项得0.5sinA=-3^0.5((1-(sinA)^2)^0.5)
(此处见sinA为负)
两边平方得0.25(sinA)^2=0.75(1-(sinA)^2)
(sinA)^2=3/4
开方得A=2kπ-π/3 A=2kπ+4π/3
f(0)=sinA+1=f(2π/3)=sin((4π/3)-A)+1
sinA=sin((4π/3)-A)=sin(4π/3)cosA-cos(4π/3)sinA/2((1-sinA)^0.5=-3^0.5/2((1-(sinA)^2)^0.5)+0.5sinA
移项得0.5sinA=-3^0.5((1-(sinA)^2)^0.5)
(此处见sinA为负)
两边平方得0.25(sinA)^2=0.75(1-(sinA)^2)
(sinA)^2=3/4
开方得A=2kπ-π/3 A=2kπ+4π/3
已知函数f(x)=sin(2x-A)+1满足f((π/3)+x)=f((π/3)-x),则A等于多少?
f(x)=sin(3x-π/4) 若函数f(x)满足方程f(x)=a(0
已知函数f(x)满足3f(x)+2f(1/x)=x+1,求f(x)
已知f(x)=2sin(2/3πx+π/6).若函数f(x)满足方程f(x)=a (1
若函数f(x)满足f(x+1)=x平方-2x,则f(根号2)等于多少
已知定义域为r的函数fx满足.f{f(x)-x+x)=f(x)-x+x ①若f(2)=3求f(1)又若f(0)=a,求f
若函数f(x)=sin(3x+φ),满足f(a+x)=f(a-x),则f(a+π6)的值为( )
已知函数f(x)=sin(ωx+φ),那函数f(2x+π/3),那等于多少?
已知函数f(x)满足f(ab)=f(a)+f(b),a,b属于R,若f(2)=3,f(3)=5,求f(36)等于多少
已知函数f(x)满足f(π+x)=f(π-x),且当x∈(0,π)时f(x)=x+cosx,则f(2),f(3),f(4
已知函数f(x)=sinπ/ 2x,则f(1)+.+f(2012)+f(2013)
已知函数f(x)满足f(ax-1)=根号(x+2)(3-x) (a不等于0)求f(x )