已知函数f(x)=acos²x–sinxcosx(x∈R)的图像经过点M(π/8,1/2),其中常数a∈R,(1)求a值及函数f(x)的最小正周期T (2)当x∈[π/8,3π/4]时,求函数f(x)的最值及相应的x值
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![已知函数f(x)=acos²x–sinxcosx(x∈R)的图像经过点M(π/8,1/2),其中常数a∈R,(1)求a值及函数f(x)的最小正周期T (2)当x∈[π/8,3π/4]时,求函数f(x)的最值及相应的x值](/uploads/image/z/10268621-53-1.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28x%29%3Dacos%26%23178%3Bx%E2%80%93sinxcosx%28x%E2%88%88R%29%E7%9A%84%E5%9B%BE%E5%83%8F%E7%BB%8F%E8%BF%87%E7%82%B9M%EF%BC%88%CF%80%2F8%2C1%2F2%EF%BC%89%2C%E5%85%B6%E4%B8%AD%E5%B8%B8%E6%95%B0a%E2%88%88R%2C%281%29%E6%B1%82a%E5%80%BC%E5%8F%8A%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%9FT+%282%29%E5%BD%93x%E2%88%88%5B%CF%80%2F8%2C3%CF%80%2F4%5D%E6%97%B6%2C%E6%B1%82%E5%87%BD%E6%95%B0f%28x%29%E7%9A%84%E6%9C%80%E5%80%BC%E5%8F%8A%E7%9B%B8%E5%BA%94%E7%9A%84x%E5%80%BC)
已知函数f(x)=acos²x–sinxcosx(x∈R)的图像经过点M(π/8,1/2),其中常数a∈R,(1)求a值及函数f(x)的最小正周期T (2)当x∈[π/8,3π/4]时,求函数f(x)的最值及相应的x值
已知函数f(x)=acos²x–sinxcosx(x∈R)的图像经过点M(π/8,1/2),其中常数a∈R,(1)求a值及函数f(x)的最小正周期T (2)当x∈[π/8,3π/4]时,求函数f(x)的最值及相应的x值
已知函数f(x)=acos²x–sinxcosx(x∈R)的图像经过点M(π/8,1/2),其中常数a∈R,(1)求a值及函数f(x)的最小正周期T (2)当x∈[π/8,3π/4]时,求函数f(x)的最值及相应的x值
f(x)=acos²x–sinxcosx
=a/2*(1+cos2x)-1/2sin2x
图像经过点M(π/8,1/2)
1/2=a/2*(1+cosπ/4)-1/2sinπ/4
1/2=a/2+a√2/4-√2/4
2=2a+a√2-√2
a(2+√2)=2+√2
a=1
f(x)=1/2cos2x-1/2sin2x+1/...
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f(x)=acos²x–sinxcosx
=a/2*(1+cos2x)-1/2sin2x
图像经过点M(π/8,1/2)
1/2=a/2*(1+cosπ/4)-1/2sinπ/4
1/2=a/2+a√2/4-√2/4
2=2a+a√2-√2
a(2+√2)=2+√2
a=1
f(x)=1/2cos2x-1/2sin2x+1/2
=√2/2cos(2x+π/4)+1/2
函数f(x)的最小正周期T =2π/2=π
(2) x∈[π/8,3π/4]
2x+π/4∈[π/2,7π/4]
cos(2x+π/4)∈[-1,√2/2]
f(x)∈[(1-√2)/2,1]
最大值=1 x=3π/4
最小值=(1-√2)/2 x=3π/8
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