如果sin^3-cos^3>cosθ-sinθ,且θ(0,2π),那么角θ的取值范围是A.(0,π/4) B.(π/2,3π) C.(π/4,5π/4) D.(5π/4,2π)
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![如果sin^3-cos^3>cosθ-sinθ,且θ(0,2π),那么角θ的取值范围是A.(0,π/4) B.(π/2,3π) C.(π/4,5π/4) D.(5π/4,2π)](/uploads/image/z/3000451-67-1.jpg?t=%E5%A6%82%E6%9E%9Csin%5E3-cos%5E3%3Ecos%CE%B8-sin%CE%B8%2C%E4%B8%94%CE%B8%EF%BC%880%2C2%CF%80%29%2C%E9%82%A3%E4%B9%88%E8%A7%92%CE%B8%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AFA.%280%2C%CF%80%2F4%29+B.%28%CF%80%2F2%2C3%CF%80%29+C.%28%CF%80%2F4%2C5%CF%80%2F4%29+D.%EF%BC%885%CF%80%2F4%2C2%CF%80%29)
如果sin^3-cos^3>cosθ-sinθ,且θ(0,2π),那么角θ的取值范围是A.(0,π/4) B.(π/2,3π) C.(π/4,5π/4) D.(5π/4,2π)
如果sin^3-cos^3>cosθ-sinθ,且θ(0,2π),那么角θ的取值范围是
A.(0,π/4) B.(π/2,3π) C.(π/4,5π/4) D.(5π/4,2π)
如果sin^3-cos^3>cosθ-sinθ,且θ(0,2π),那么角θ的取值范围是A.(0,π/4) B.(π/2,3π) C.(π/4,5π/4) D.(5π/4,2π)
(sinθ)^3-(cosθ)^3=(sinθ-cosθ)((sinθ)^2+sinθ*cosθ+(cosθ)^2)
=(sinθ-cosθ)(1+sinθ*cosθ)
(sinθ)^3-(cosθ)^3-(cosθ-sinθ)
=(sinθ-cosθ)(2+sinθ*cosθ)>0
因为2+sinθ*cosθ=2+sin2θ/2>0
所以sinθ-cosθ>0
所以sin(θ-π/4)=sinθ*√2/2-cosθ*√2/2>0
所以C.(π/4,5π/4)