已知函数f(x)=cosx(sinx+cosx)-1/2若0<α<π/2,且sinα=(根号2)/2 求f(α)的值求函数f(x)的最小正周期及单调递增区间
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![已知函数f(x)=cosx(sinx+cosx)-1/2若0<α<π/2,且sinα=(根号2)/2 求f(α)的值求函数f(x)的最小正周期及单调递增区间](/uploads/image/z/3858501-21-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dcosx%28sinx%2Bcosx%29-1%2F2%E8%8B%A50%EF%BC%9C%CE%B1%EF%BC%9C%CF%80%2F2%2C%E4%B8%94sin%CE%B1%3D%EF%BC%88%E6%A0%B9%E5%8F%B72%EF%BC%89%2F2++++%E6%B1%82f%28%CE%B1%EF%BC%89%E7%9A%84%E5%80%BC%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E5%8F%8A%E5%8D%95%E8%B0%83%E9%80%92%E5%A2%9E%E5%8C%BA%E9%97%B4)
已知函数f(x)=cosx(sinx+cosx)-1/2若0<α<π/2,且sinα=(根号2)/2 求f(α)的值求函数f(x)的最小正周期及单调递增区间
已知函数f(x)=cosx(sinx+cosx)-1/2
若0<α<π/2,且sinα=(根号2)/2 求f(α)的值
求函数f(x)的最小正周期及单调递增区间
已知函数f(x)=cosx(sinx+cosx)-1/2若0<α<π/2,且sinα=(根号2)/2 求f(α)的值求函数f(x)的最小正周期及单调递增区间
f(x)=sinxcosx+cos²x-1/2
=1/2*sin2x+1/2*(1+cos2x)-1/2
=1/2*sin2x+1/2*cos2x
=√2/2*(√2/2*sin2x+√2/2*cos2x)
=√2/2*sin(2x+π/4)
(1)∵0
f(x)=cos²x+sinxcosx-1/2
=(1+cos2x)/2+(sin2x)/2-1/2
=1/2(sin2x+cos2x)
=√2/2sin(2x+π/4)
最大值2x+π/4=π/2 x=π/8+2kπ 最小值x=5π/8+2kπ
0<α<π/2,sinα=(根号2)/2
α=π/4
f(α)=cosπ/4(sinπ/4+cosπ/4)-1/2
=√2/2(√2/2+√2/2)-1/2
=1/2
f(x)=cosx(sinx+cosx)-1/2
=sinxcosx+cos^2x-1/2
=1/2sin2x+(cos2x+1)/2-1/2
=1/2(sin2x+c...
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0<α<π/2,sinα=(根号2)/2
α=π/4
f(α)=cosπ/4(sinπ/4+cosπ/4)-1/2
=√2/2(√2/2+√2/2)-1/2
=1/2
f(x)=cosx(sinx+cosx)-1/2
=sinxcosx+cos^2x-1/2
=1/2sin2x+(cos2x+1)/2-1/2
=1/2(sin2x+cos2x)
=√2/2sin(2x+π/4)
T=2π/2=π
-π/2+2kπ<2x+π/4<π/2+2kπ
-3π/4+2kπ<2x<π/4+2kπ
单增区间:-3π/8+kπ
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