已知函数f(x)=根号3cos(-π-x/2)sin(3π+x/2)-cos² x/2+1用五点作图法,做出函数f(x)在【0,2π】上的简图(这个我不会啊啊啊)若x属于【0,π/2】,f(x)=11/10,求cosx的值
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![已知函数f(x)=根号3cos(-π-x/2)sin(3π+x/2)-cos² x/2+1用五点作图法,做出函数f(x)在【0,2π】上的简图(这个我不会啊啊啊)若x属于【0,π/2】,f(x)=11/10,求cosx的值](/uploads/image/z/12526872-24-2.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3D%E6%A0%B9%E5%8F%B73cos%EF%BC%88-%CF%80-x%2F2%EF%BC%89sin%EF%BC%883%CF%80%2Bx%2F2%EF%BC%89-cos%26%23178%3B+x%2F2%2B1%E7%94%A8%E4%BA%94%E7%82%B9%E4%BD%9C%E5%9B%BE%E6%B3%95%2C%E5%81%9A%E5%87%BA%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%E5%9C%A8%E3%80%900%2C2%CF%80%E3%80%91%E4%B8%8A%E7%9A%84%E7%AE%80%E5%9B%BE%EF%BC%88%E8%BF%99%E4%B8%AA%E6%88%91%E4%B8%8D%E4%BC%9A%E5%95%8A%E5%95%8A%E5%95%8A%EF%BC%89%E8%8B%A5x%E5%B1%9E%E4%BA%8E%E3%80%900%2C%CF%80%2F2%E3%80%91%2Cf%EF%BC%88x%EF%BC%89%3D11%2F10%2C%E6%B1%82cosx%E7%9A%84%E5%80%BC)
已知函数f(x)=根号3cos(-π-x/2)sin(3π+x/2)-cos² x/2+1用五点作图法,做出函数f(x)在【0,2π】上的简图(这个我不会啊啊啊)若x属于【0,π/2】,f(x)=11/10,求cosx的值
已知函数f(x)=根号3cos(-π-x/2)sin(3π+x/2)-cos² x/2+1
用五点作图法,做出函数f(x)在【0,2π】上的简图(这个我不会啊啊啊)
若x属于【0,π/2】,f(x)=11/10,求cosx的值
已知函数f(x)=根号3cos(-π-x/2)sin(3π+x/2)-cos² x/2+1用五点作图法,做出函数f(x)在【0,2π】上的简图(这个我不会啊啊啊)若x属于【0,π/2】,f(x)=11/10,求cosx的值
已知函数f(x)=(√3)cos(-π-x/2)sin(3π+x/2)-cos² (x/2)+1
用五点作图法,做出函数f(x)在【0,2π】上的简图;
若x属于【0,π/2】,f(x)=11/10,求cosx的值
f(x)=(√3)cos(π+x/2)sin(π+x/2)-cos²( x/2)+1=(√3)[-cos(x/2)][-sin(x/2)]-(1+cosx)/2+1
=(√3/2)sinx-(1/2)cosx+1/2=sinxcos(π/6)-cosxsin(π/6)+1/2=sin(x-π/6)+1/2
用五点作图法,先列表:
x-π/6 0 π/2 π 3π/2 2π 【共五点】
x π/6 4π/6 7π/6 10π/6 13π/6 【不要约简,保留公分母6,好画图】
sin(x-π/6) 0 1 0 -1 0
sin(x-π/6)+1/2 1/2 3/2 1/2 -1/2 1/2
作图:横坐标以π/6≈0.5作单位长,上面五个点的间距都是3个单位长.纵坐标以1为单位长.
在坐标纸上描出上面五点(π/6,1/2); (2π/3,3/2);(7π/6,1/2);(5π/3,-1/2);(13π/6,1/2).
把五个点光滑的连接起来,再把原点(0,0)与(π/6,1/2)连接起来;最后一点13π/6-π/6=2π,即前面所连曲线与x轴的交点就是(2π,0);在图上把横坐标0,π/6,2π/3,7π/6,5π/3,2π都标出来;再把纵坐标上的1/2,3/2标出来,图就作好啦!
f(x)=sin(x-π/6)+1/2=11/10,故得sin(x-π/6)=11/10-1/2=6/10=3/5,
即有x-π/6=arcsin(3/5),x=(π/6)+arcsin(3/5)
故cosx=cos[π/6+arcsin(3/5)]=cos(π/6)cos[arcsin(3/5)]-sin(π/6)sin[arcsin(3/5)]
=(√3/2)√(1-9/25)-(1/2)(3/5)=4√3/10-3/10=(1/10)(4√3-3).
【其中cosarcsin(3/5)=√[1-(3/5)²]=√(16/25)=4/5;sinarcsin(3/5)=3/5】
我真的不会啊