已知sin(A+π/4)=7根号2/10,A∈(π/4,π/2).求cosA的值,求函数f(x)=cos2x+5/2sinAsinx的值域复制搜索
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![已知sin(A+π/4)=7根号2/10,A∈(π/4,π/2).求cosA的值,求函数f(x)=cos2x+5/2sinAsinx的值域复制搜索](/uploads/image/z/3878153-17-3.jpg?t=%E5%B7%B2%E7%9F%A5sin%EF%BC%88A%2B%CF%80%2F4%EF%BC%89%3D7%E6%A0%B9%E5%8F%B72%2F10%2CA%E2%88%88%EF%BC%88%CF%80%2F4%2C%CF%80%2F2%EF%BC%89.%E6%B1%82cosA%E7%9A%84%E5%80%BC%2C%E6%B1%82%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3Dcos2x%2B5%2F2sinAsinx%E7%9A%84%E5%80%BC%E5%9F%9F%E5%A4%8D%E5%88%B6%E6%90%9C%E7%B4%A2)
已知sin(A+π/4)=7根号2/10,A∈(π/4,π/2).求cosA的值,求函数f(x)=cos2x+5/2sinAsinx的值域复制搜索
已知sin(A+π/4)=7根号2/10,A∈(π/4,π/2).求cosA的值,
求函数f(x)=cos2x+5/2sinAsinx的值域
复制搜索
已知sin(A+π/4)=7根号2/10,A∈(π/4,π/2).求cosA的值,求函数f(x)=cos2x+5/2sinAsinx的值域复制搜索
sin(A+π/4)=7√2/10,
A属于(π/4,π/2)
cos(A+π/4)
=-√2/10
cosA=cos[(A+π/4)-π/4]
=cos(A+π/4)cosπ/4+sin(A+π/4)sinπ/4
=(-√2/10)*(√2/2)+(7√2/10)*(√2/2)=3/5
A∈(π/4,π/2),所以sinA=4/5,
f(x)=cos2x+5/2sinAsinx
= cos2x+2sinx
=1-2sin²x+2sinx
=-2(sinx-1/2)²+3/2
Sinx=1/2时,函数取到最大值3/2.
Sinx=-1时,函数取到最小值-3.
所以函数值域是[-3,3/2].
sin(A+π/4)=7√2/10,
A属于(π/4,π/2)
cos(A+π/4)
=-√2/10
cosA=cos[(A+π/4)-π/4]
=cos(A+π/4)cosπ/4+sin(A+π/4)sinπ/4
=(-√2/10)*(√2/2)+(7√2/10)*(√2/2)=3/5
A∈(π/4,π/2),所以...
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sin(A+π/4)=7√2/10,
A属于(π/4,π/2)
cos(A+π/4)
=-√2/10
cosA=cos[(A+π/4)-π/4]
=cos(A+π/4)cosπ/4+sin(A+π/4)sinπ/4
=(-√2/10)*(√2/2)+(7√2/10)*(√2/2)=3/5
A∈(π/4,π/2),所以sinA=4/5,
f(x)=cos2x+5/2sinAsinx
= cos2x+2sinx
=1-2sin²x+2sinx
=-2(sinx-1/2)²+3/2
sinx的值域是(-1,1)
Sinx=1/2时,函数取到最大值3/2.
Sinx=-1时,函数取到最小值-3.
所以函数值域是[-3,3/2].
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