how to find period of a function!!?? BE QUICK PLZ!!!!!

2006-10-15 4:10 am
If the function is given as

f(x)=sin(x)cos(2x)+1

and it is known that the function is periodic, then how can I know the exact period of that function!?

any graphic solution or software cannot be used, just solve it matermatically!!
更新1:

to hckchn,still havent solved it, I dun think your equation is going to work and be able to show what eactly T is the graphical solution show the period is roughtly ~5.3 rather than 6.28 , which is definitely not equal to 2 pie much apperciated if there are some more better suggestion~~

回答 (2)

2006-10-15 9:07 am
✔ 最佳答案
when x=π/2,f(x)=0
whenx=π.f(x)=1
when x=3π/2,f(x)=2
whenx=2π,f(x)=1
whenx=5π/2,f(X)=0 again

so the so the period=5π/2-π/2=2

2006-10-15 01:07:50 補充:
it should be 2π,sorry
參考: me
2006-10-15 8:07 am
Let period be T
f(x)=f(x+T)
sin(x)cos(2x)+1 = sin(x+T)cos(2x+2T) +1
sin(x)cos(2x)=sin(x+T)cos(2x+2T)
sinxcos2x = [sinxcosT+sinTcosx][cos2xcos2T-sinxsin2T]
sinxcos2x =sinxcos2xcosTcos2T +sinTcosxcos2xcos2T - sinxcosTsinxsin2T - sinTcosxsinxsin2T


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