一道数学题:已知函数f(t)=√[(1-t)/(1+t)],g(x)=cosx*f(sinx)+sinx*f(cosx),x属于(π,17π/12)已知函数f(t)=√[(1-t)/(1+t)],g(x)=cosx*f(sinx)+sinx*f(cosx),x属于(π,17π/12).(1)将函数g(x)化简成Asin(ωx+φ)+B(A>0
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![一道数学题:已知函数f(t)=√[(1-t)/(1+t)],g(x)=cosx*f(sinx)+sinx*f(cosx),x属于(π,17π/12)已知函数f(t)=√[(1-t)/(1+t)],g(x)=cosx*f(sinx)+sinx*f(cosx),x属于(π,17π/12).(1)将函数g(x)化简成Asin(ωx+φ)+B(A>0](/uploads/image/z/1618623-63-3.jpg?t=%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%EF%BC%9A%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28t%29%3D%E2%88%9A%5B%281-t%29%2F%281%2Bt%29%5D%2Cg%28x%29%3Dcosx%2Af%28sinx%29%2Bsinx%2Af%28cosx%29%2Cx%E5%B1%9E%E4%BA%8E%EF%BC%88%CF%80%2C17%CF%80%2F12%EF%BC%89%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28t%29%3D%E2%88%9A%5B%281-t%29%2F%281%2Bt%29%5D%2Cg%28x%29%3Dcosx%2Af%28sinx%29%2Bsinx%2Af%28cosx%29%2Cx%E5%B1%9E%E4%BA%8E%EF%BC%88%CF%80%2C17%CF%80%2F12%EF%BC%89.%EF%BC%881%EF%BC%89%E5%B0%86%E5%87%BD%E6%95%B0g%28x%29%E5%8C%96%E7%AE%80%E6%88%90Asin%EF%BC%88%CF%89x%2B%CF%86%EF%BC%89%2BB%EF%BC%88A%EF%BC%9E0)
一道数学题:已知函数f(t)=√[(1-t)/(1+t)],g(x)=cosx*f(sinx)+sinx*f(cosx),x属于(π,17π/12)已知函数f(t)=√[(1-t)/(1+t)],g(x)=cosx*f(sinx)+sinx*f(cosx),x属于(π,17π/12).(1)将函数g(x)化简成Asin(ωx+φ)+B(A>0
一道数学题:已知函数f(t)=√[(1-t)/(1+t)],g(x)=cosx*f(sinx)+sinx*f(cosx),x属于(π,17π/12)
已知函数f(t)=√[(1-t)/(1+t)],g(x)=cosx*f(sinx)+sinx*f(cosx),x属于(π,17π/12).
(1)将函数g(x)化简成Asin(ωx+φ)+B(A>0,ω>0,φ∈[0,2π))的形式,
(2)求函数g(x)的值域.
这个我看过了,看不懂
一道数学题:已知函数f(t)=√[(1-t)/(1+t)],g(x)=cosx*f(sinx)+sinx*f(cosx),x属于(π,17π/12)已知函数f(t)=√[(1-t)/(1+t)],g(x)=cosx*f(sinx)+sinx*f(cosx),x属于(π,17π/12).(1)将函数g(x)化简成Asin(ωx+φ)+B(A>0
f(t) = [(1-t)/(1+t)]^(1/2),
定义域,
(1 - t)/(1 + t) >= 0,t 不等于 -1.
(1-t)(1+t) >= 0,
-1 < t sin(x + π/4) > sin(3π/2) = -1
-1 > 2^(1/2)sin(x + π/4) > -2^(1/2)
-3 > 2^(1/2)sin(x + π/4) - 2 = g(x) > -2 - 2^(1/2)
所以,
函数g(x)的值域为(-2-2^(1/2),-3)
那个过程已经很详细了,这个问题是一个复合函数的问题,你可以再看一下课本再来理解这题