已知向量m=(sinx,1),向量n=(√3cosx,1/2),函数f(x)=(m+n)·m.(1)求f(x)的最小正周期T及单调递增区间(2)已知a,b,c,分别为△ABC内角A,B,C的对边,A为锐角,a=2√3,c=4,且f(A)是函数f(x)在【0,π/2】上的最大值,求△A
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![已知向量m=(sinx,1),向量n=(√3cosx,1/2),函数f(x)=(m+n)·m.(1)求f(x)的最小正周期T及单调递增区间(2)已知a,b,c,分别为△ABC内角A,B,C的对边,A为锐角,a=2√3,c=4,且f(A)是函数f(x)在【0,π/2】上的最大值,求△A](/uploads/image/z/1042174-46-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fm%3D%28sinx%2C1%29%2C%E5%90%91%E9%87%8Fn%3D%28%E2%88%9A3cosx%2C1%2F2%29%2C%E5%87%BD%E6%95%B0f%28x%29%3D%28m%2Bn%29%C2%B7m.%281%29%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9FT%E5%8F%8A%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4%282%29%E5%B7%B2%E7%9F%A5a%2Cb%2Cc%2C%E5%88%86%E5%88%AB%E4%B8%BA%E2%96%B3ABC%E5%86%85%E8%A7%92A%2CB%2CC%E7%9A%84%E5%AF%B9%E8%BE%B9%2CA%E4%B8%BA%E9%94%90%E8%A7%92%2Ca%3D2%E2%88%9A3%2Cc%3D4%2C%E4%B8%94f%28A%29%E6%98%AF%E5%87%BD%E6%95%B0f%EF%BC%88x%29%E5%9C%A8%E3%80%900%2C%CF%80%2F2%E3%80%91%E4%B8%8A%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%2C%E6%B1%82%E2%96%B3A)
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已知向量m=(sinx,1),向量n=(√3cosx,1/2),函数f(x)=(m+n)·m.(1)求f(x)的最小正周期T及单调递增区间(2)已知a,b,c,分别为△ABC内角A,B,C的对边,A为锐角,a=2√3,c=4,且f(A)是函数f(x)在【0,π/2】上的最大值,求△A
已知向量m=(sinx,1),向量n=(√3cosx,1/2),函数f(x)=(m+n)·m.(1)求f(x)的最小正周期T及单调递增区间
(2)已知a,b,c,分别为△ABC内角A,B,C的对边,A为锐角,a=2√3,c=4,且f(A)是函数f(x)在【0,π/2】上的最大值,求△ABC的面积S
已知向量m=(sinx,1),向量n=(√3cosx,1/2),函数f(x)=(m+n)·m.(1)求f(x)的最小正周期T及单调递增区间(2)已知a,b,c,分别为△ABC内角A,B,C的对边,A为锐角,a=2√3,c=4,且f(A)是函数f(x)在【0,π/2】上的最大值,求△A
f(x)
= (m+n).n
= (sinx+√3cosx)sinx + (3/2)
= (sinx)^2 + √3/2sin2x + 3/2
= (1-cos2x)/2+ √3/2sin2x + 3/2
=-cos2x/2 + √3/2sin2x + 2
= sin(2x-30°) + 2
最小正周期 = 90°
单调递增区间:
360°k -90°