设M(cosπx3+cosπx5，sinπx3+sinπx5)（x∈R）为坐标平面内一点，O为坐标原点，记f（x）=|OM|，当x变化时，函数f（x）的最小正周期是（）A．30πB．15πC．30D．15

Question

设M(cos(πx)/(3)+cos(πx)/(5)，sin(πx)/(3)+sin(πx)/(5))（x∈R）为坐标平面内一点，O为坐标原点，记f（x）=|OM|，当x变化时，函数f（x）的最小正周期是（　　）

A．30π
B．15π
C．30
D．15M(cos(πx)/(3)+cos(πx)/(5)，sin(πx)/(3)+sin(πx)/(5))（x∈R）为坐标平面内一点，O为坐标原点，记f（x）=|OM|，当x变化时，函数f（x）的最小正周期是（　　）

A．30π
B．15π
C．30
D．15(πx)/(3)πxπx33(πx)/(5)πxπx55(πx)/(3)πxπx33(πx)/(5)πxπx55

Answer 1

∵f（x）=|OM|
=√((cos(πx)/(3)+cos(πx)/(5))2+(sin(πx)/(3)+sin(πx)/(5))2)
=√(cos((2π)/(15)x)+2)
∵ω=(2π)/(15)
故T=(2π)/(ω)=15
故选D √((cos(πx)/(3)+cos(πx)/(5))2+(sin(πx)/(3)+sin(πx)/(5))2)

(cos(πx)/(3)+cos(πx)/(5))2+(sin(πx)/(3)+sin(πx)/(5))2

(cos(πx)/(3)+cos(πx)/(5))2+(sin(πx)/(3)+sin(πx)/(5))2(cos(πx)/(3)πxπxπx333+cos(πx)/(5)πxπxπx555)2+(sin(πx)/(3)+sin(πx)/(5))22+(sin(πx)/(3)πxπxπx333+sin(πx)/(5)πxπxπx555)22
=√(cos((2π)/(15)x)+2)
∵ω=(2π)/(15)
故T=(2π)/(ω)=15
故选D √(cos((2π)/(15)x)+2)

cos((2π)/(15)x)+2

cos((2π)/(15)x)+2cos((2π)/(15)2π2π2π151515x)+2
∵ω=(2π)/(15)
故T=(2π)/(ω)=15
故选D (2π)/(15)2π2π2π151515
故T=(2π)/(ω)=15
故选D (2π)/(ω)2π2π2πωωω=15
故选D