f(x)=2sin(x/4)cos(x/4)+√3cos(x/2).求f(x)最小正周期.令g(x)=f(x+∏/3)判断g(x)奇偶性
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![f(x)=2sin(x/4)cos(x/4)+√3cos(x/2).求f(x)最小正周期.令g(x)=f(x+∏/3)判断g(x)奇偶性](/uploads/image/z/12525131-11-1.jpg?t=f%28x%29%3D2sin%28x%2F4%29cos%28x%2F4%29%2B%E2%88%9A3cos%28x%2F2%29.%E6%B1%82f%28x%29%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F.%E4%BB%A4g%28x%29%3Df%28x%2B%E2%88%8F%2F3%29%E5%88%A4%E6%96%ADg%28x%29%E5%A5%87%E5%81%B6%E6%80%A7)
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f(x)=2sin(x/4)cos(x/4)+√3cos(x/2).求f(x)最小正周期.令g(x)=f(x+∏/3)判断g(x)奇偶性
f(x)=2sin(x/4)cos(x/4)+√3cos(x/2).求f(x)最小正周期.令g(x)=f(x+∏/3)判断g(x)奇偶性
f(x)=2sin(x/4)cos(x/4)+√3cos(x/2).求f(x)最小正周期.令g(x)=f(x+∏/3)判断g(x)奇偶性
(x)=2sin(x/4)cos(x/4)+√3cos(x/2)=sin(x/2)+√3cos(x/2)=2sin(x/2+pi/3)
T=4pi
g(x)=2sin(x/2+pi/2)=2cos(x/2)
偶函数
2sin(x/4)cos(x/4)=sin(x/2)
然后提取2,得2(1/2sin(x/2)+根号3cos(x/2))=2sin(x/2+60)
T=4π
判断奇偶就带进去就好了
f(x)=sin(x/2)+√3cos(x/2)
=2sin(x/2+arctan√3)
=2sin(x/2+π/3)
T=2π/(1/2)=4π
g(x)=f(x+π/3)=2sin[(x+π/3)/2+π/3]
=2sin(x/2+π/2)
=2cos(x/2)
g(-x)=2cos(-x/2)=2cos(x/2)=g(x)
且定义域x属于R,关于原点对称
所以是偶函数
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