已知向量a=( sin(1/2)x,(根号3)/2 ).向量b=( 1/2,cos(1/2)x ),f(x)=向量a·向量b,(1)求函数y=f(x)已知向量a=( sin(1/2)x,(根号3)/2 ).向量b=( 1/2,cos(1/2)x ),f(x)=向量a·向量b,(1)求函数y=f(x)的最小正周期及最大值
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![已知向量a=( sin(1/2)x,(根号3)/2 ).向量b=( 1/2,cos(1/2)x ),f(x)=向量a·向量b,(1)求函数y=f(x)已知向量a=( sin(1/2)x,(根号3)/2 ).向量b=( 1/2,cos(1/2)x ),f(x)=向量a·向量b,(1)求函数y=f(x)的最小正周期及最大值](/uploads/image/z/2523879-63-9.jpg?t=%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28+sin%281%2F2%29x%2C%28%E6%A0%B9%E5%8F%B73%29%2F2+%29.%E5%90%91%E9%87%8Fb%3D%28+1%2F2%2Ccos%281%2F2%29x+%29%2Cf%28x%29%3D%E5%90%91%E9%87%8Fa%C2%B7%E5%90%91%E9%87%8Fb%2C%EF%BC%881%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0y%3Df%28x%29%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%28+sin%281%2F2%29x%2C%28%E6%A0%B9%E5%8F%B73%29%2F2+%29.%E5%90%91%E9%87%8Fb%3D%28+1%2F2%2Ccos%281%2F2%29x+%29%2Cf%28x%29%3D%E5%90%91%E9%87%8Fa%C2%B7%E5%90%91%E9%87%8Fb%2C%EF%BC%881%EF%BC%89%E6%B1%82%E5%87%BD%E6%95%B0y%3Df%28x%29%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F%E5%8F%8A%E6%9C%80%E5%A4%A7%E5%80%BC)
已知向量a=( sin(1/2)x,(根号3)/2 ).向量b=( 1/2,cos(1/2)x ),f(x)=向量a·向量b,(1)求函数y=f(x)已知向量a=( sin(1/2)x,(根号3)/2 ).向量b=( 1/2,cos(1/2)x ),f(x)=向量a·向量b,(1)求函数y=f(x)的最小正周期及最大值
已知向量a=( sin(1/2)x,(根号3)/2 ).向量b=( 1/2,cos(1/2)x ),f(x)=向量a·向量b,(1)求函数y=f(x)
已知向量a=( sin(1/2)x,(根号3)/2 ).向量b=( 1/2,cos(1/2)x ),f(x)=向量a·向量b,
(1)求函数y=f(x)的最小正周期及最大值
(2)求函数y=f(x)的单调递增区间
已知向量a=( sin(1/2)x,(根号3)/2 ).向量b=( 1/2,cos(1/2)x ),f(x)=向量a·向量b,(1)求函数y=f(x)已知向量a=( sin(1/2)x,(根号3)/2 ).向量b=( 1/2,cos(1/2)x ),f(x)=向量a·向量b,(1)求函数y=f(x)的最小正周期及最大值
(1)
∵向量a=( sin(1/2)x,(√3)/2 ),向量b=( 1/2,cos(1/2)x )
∴f(x)=向量a·向量b=(1/2)sin(1/2)x+[(√3)/2 ]cos(1/2)x =sin(x/2+π/3)
∴函数y=f(x)的最小正周期T=2π/(1/2)=4π.
当且仅当x/2+π/3=π/2+2kπ(k∈Z),即x=π/3+4kπ(k∈Z)时,f(x)取得最大值1.
(2)
令-π/2+2kπ≤x/2+π/3≤π/2+2kπ(k∈Z),即-5π/3+4kπ≤x≤π/3+4kπ(k∈Z).
则函数y=f(x)的单调递增区间为-5π/3+4kπ≤x≤π/3+4kπ(k∈Z).