已知函数f(X)=sin(2x+π/6)+sin(2x-π/6)+2cos平方X(1)求f(x)的最大值及最正周期;(2)求使f(x)>=2的x的取值范围
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 02:08:25
![已知函数f(X)=sin(2x+π/6)+sin(2x-π/6)+2cos平方X(1)求f(x)的最大值及最正周期;(2)求使f(x)>=2的x的取值范围](/uploads/image/z/1628038-46-8.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28X%29%3Dsin%282x%2B%CF%80%2F6%29%2Bsin%282x-%CF%80%2F6%29%2B2cos%E5%B9%B3%E6%96%B9X%EF%BC%881%EF%BC%89%E6%B1%82f%28x%29%E7%9A%84%E6%9C%80%E5%A4%A7%E5%80%BC%E5%8F%8A%E6%9C%80%E6%AD%A3%E5%91%A8%E6%9C%9F%EF%BC%9B%EF%BC%882%EF%BC%89%E6%B1%82%E4%BD%BFf%28x%29%3E%3D2%E7%9A%84x%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4)
已知函数f(X)=sin(2x+π/6)+sin(2x-π/6)+2cos平方X(1)求f(x)的最大值及最正周期;(2)求使f(x)>=2的x的取值范围
已知函数f(X)=sin(2x+π/6)+sin(2x-π/6)+2cos平方X(1)求f(x)的最大值及最正周期;(2)求使f(x)>=2的x的取值范围
已知函数f(X)=sin(2x+π/6)+sin(2x-π/6)+2cos平方X(1)求f(x)的最大值及最正周期;(2)求使f(x)>=2的x的取值范围
f(x)=sin(2x+π/6)+sin(2x-π/6)+2cos²x=2sin2x*cosπ/6+2cos²x=√3sin2x+2cos²x=√3sin2x+cos2x+1=2sin(2x+π/6)+1.
(1).f(x)max=2+1=3,T=2π/2=π.
(2).f(x)≥2可化为sin(2x+π/6)≥1/2,解得kπ≤x≤kπ+π/3.(k属于整数)
先化简:f(X)=sin2xcosπ/6+cos2xsinπ/6+sin2xcosπ/6-cos2xsinπ/6+ 2cos平方X
=2sin2xcosπ/6+2cos平方X
=√3sin2x+2cos平方X
=√3s...
全部展开
先化简:f(X)=sin2xcosπ/6+cos2xsinπ/6+sin2xcosπ/6-cos2xsinπ/6+ 2cos平方X
=2sin2xcosπ/6+2cos平方X
=√3sin2x+2cos平方X
=√3sin2x+cos2X
=2sin(2X+π/6)+1
(1)最大值为3 周期为π
(2)当2sin(2X+π/6)+1=2时
X=(kπ)/2或π/3 +kπ
取值范围:π/2 +2kπ<=x<= 4π/3+2kπ
取值范围:
收起