The minimum positive period of f x sinx 4 cos 4 is

Proof of: (1) f(x+2 )=sin(x+2 )=sinx=f(x)2) Suppose there is 0 t 2 so that f(x+t)=f(x) i.e. sin(x+t)=sinx,x r

Let x=0, then sint=0and 0 t Mingda Ye 2, then t =Let x=,sin(+t)=sin i.e. sin=sin, which is a contradiction.

From the two steps of the macro (1) and (2), it can be seen that 2 is the minimum positive period of f(x)=sinx.

Whether f(x)=4sin(3x)+cos(3x) is a periodic function and what is the minimum positive period.

The minimum positive period t=2 1 3 =6

2( 2 Shen Fan Pai Kuan Xian 2*sinx- 2 2*cosx) 2(sinxcos 4-cosxsin sedan jujube 4) 2*sin(x- 4).

The minimum positive period of f(x)=sinx-cosx is: t=2 1=2 ;

f(x)=sin^4x+cos^2x

1-sin^2x+sin^4x

sin^2x(sin^2-1)+1

sin^2xcos^2x+1

1/2sin2x)^2+1

1 Car number: 8 (1-cos4x) + 1

7 Closed imitation first 8+1 8cos4x

The minimum positive period is 1 2

f(x)=(sinx)^4+(cosx)^4=[(sinx)^2+(cosx)^2]^2

2(sinx)^2(cosx)^2=1

sin(2x)] 2 Short2=1-[1-cos(4x)] 4=cos(4x) 4

3 42 = 2 functions.

Minimum positive period.

For 2, it is late to bury it.

First of all, write the solution: original formula = [cos 2(x)] 2-[sin 2(x)] 2+5[1 no boy 2(cos2x+1)] 2-[1 2(1-cos2x)] 2+5

1/4[(cos2x+1)^2-(cos2x-1)^2]+51/4*4cos2x)+5

cos2x+5

The fastest key to get the answer seems to have brought the wrong draft to check the formula, and the cycle is

f(x)=cos4x-sin4x=root number 2 cos(4x 4).

So the minimum positive period is 2 4= 2

f(x)=(sinx 2+cosx 2) 2-2sinx 2cosx 2=1-sin2x 2 muffled mountain 2=1-(1-cos4x) 4=3 4+cos4x

Therefore, the minimum curve is 2 4 = 2