已知函数fx=Asin(x+ψ)(A>0,0<ψ<π)x属于R的最大值是1,其图像过点M(π/3,1/2)求fx的解析式我已知晓答案为:最大则A=1过Msin(π/3+ψ)=1/2π/3+ψ=5π/6ψ=π/2所以f(x)=sin(x+π/2)即f(x)=cosx只是不明白
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![已知函数fx=Asin(x+ψ)(A>0,0<ψ<π)x属于R的最大值是1,其图像过点M(π/3,1/2)求fx的解析式我已知晓答案为:最大则A=1过Msin(π/3+ψ)=1/2π/3+ψ=5π/6ψ=π/2所以f(x)=sin(x+π/2)即f(x)=cosx只是不明白](/uploads/image/z/2623483-19-3.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0fx%3DAsin%EF%BC%88x%2B%CF%88%EF%BC%89%EF%BC%88A%EF%BC%9E0%2C0%EF%BC%9C%CF%88%EF%BC%9C%CF%80%EF%BC%89x%E5%B1%9E%E4%BA%8ER%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E6%98%AF1%2C%E5%85%B6%E5%9B%BE%E5%83%8F%E8%BF%87%E7%82%B9M%EF%BC%88%CF%80%2F3%2C1%2F2%EF%BC%89%E6%B1%82fx%E7%9A%84%E8%A7%A3%E6%9E%90%E5%BC%8F%E6%88%91%E5%B7%B2%E7%9F%A5%E6%99%93%E7%AD%94%E6%A1%88%E4%B8%BA%EF%BC%9A%E6%9C%80%E5%A4%A7%E5%88%99A%3D1%E8%BF%87Msin%28%CF%80%2F3%2B%CF%88%29%3D1%2F2%CF%80%2F3%2B%CF%88%3D5%CF%80%2F6%CF%88%3D%CF%80%2F2%E6%89%80%E4%BB%A5f%28x%29%3Dsin%28x%2B%CF%80%2F2%29%E5%8D%B3f%28x%29%3Dcosx%E5%8F%AA%E6%98%AF%E4%B8%8D%E6%98%8E%E7%99%BD)
已知函数fx=Asin(x+ψ)(A>0,0<ψ<π)x属于R的最大值是1,其图像过点M(π/3,1/2)求fx的解析式我已知晓答案为:最大则A=1过Msin(π/3+ψ)=1/2π/3+ψ=5π/6ψ=π/2所以f(x)=sin(x+π/2)即f(x)=cosx只是不明白
已知函数fx=Asin(x+ψ)(A>0,0<ψ<π)x属于R的最大值是1,其图像过点M(π/3,1/2)求fx的解析式
我已知晓答案为:最大则A=1
过M
sin(π/3+ψ)=1/2
π/3+ψ=5π/6
ψ=π/2
所以f(x)=sin(x+π/2)
即f(x)=cosx
只是不明白π/3+ψ=5π/6这一步,不应该是π/3+ψ=π/6+2kπ吗?我知道这是根据sin(π-a)=sina,可是一般的不都是用π/3+ψ=π/6+2kπ来解吗?可是用这个却解不出,
已知函数fx=Asin(x+ψ)(A>0,0<ψ<π)x属于R的最大值是1,其图像过点M(π/3,1/2)求fx的解析式我已知晓答案为:最大则A=1过Msin(π/3+ψ)=1/2π/3+ψ=5π/6ψ=π/2所以f(x)=sin(x+π/2)即f(x)=cosx只是不明白
A=1
f(π/3)=sin(π/3+ψ)=1/2
π/3+ψ=π/6+2kπ 或5π/6+2kπ
ψ=-π/6+2kπ或π/2+2kπ k∈z
0<ψ<π
∴ψ=π/2
f(x)=sin(x+π/2)
f(x)=cosx
∵sin(π/3+ψ)=1/2
可以为30°或150°
fx=sin(x+π/2)
∵f(x)最大值是1,A>0
∴A=1
∵图像过点M(π/3,1/2)
∴f(π/3)=sin(π/3+ψ)=1/2
∵0<ψ<π
∴π/3<π/3+ψ<4π/3
∴π/3+ψ=5π/6
∴ψ=π/2
∴f(x)=sin(x+π/2) =cosx只是不明白π/3+ψ=5π/6这一步,不应该是π/3+ψ=π/6+2kπ吗?我知道这是根...
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∵f(x)最大值是1,A>0
∴A=1
∵图像过点M(π/3,1/2)
∴f(π/3)=sin(π/3+ψ)=1/2
∵0<ψ<π
∴π/3<π/3+ψ<4π/3
∴π/3+ψ=5π/6
∴ψ=π/2
∴f(x)=sin(x+π/2) =cosx
收起
因为sin5π|6=1|2