Y 2sinx Monotonic reduction interval of sinx cosx process 5

2(sinx)2+2sinxcosx

2(1-(cosx)2)+sin2x

2(1-(1+cos2x/2))+sin2xsin2x+cos2x+1

Root 2sin (2x + pai 4) + 1

Therefore, the monotonic increase interval is -3 8 Pai + 2 kPai to Pai 8 + 2 kPai The monotonically decreasing interval is Pai 8 + 2 kPai to 5 Pai 8 + 2 kPai

The original formula can be reduced to y=1-cos(2x)+sin(2x)=1+ 2sin(

Then see for yourself.

The transformation of half and double angles is too retarded.

y=2sinxcosx+2sinxsinxsin2x-cos2x+1

1+√2sin(2x-π/4)

1+√2sin2x-1

2sin2x formula: sin2x=2sinx*cosxcos2x=1-2sinx*sinx=2cosx*cosx-1cosxcosx-sinxsinx

This is the formula for the double angle, so you can use this in the future.

What is the monotonically decreasing interval of y=sin(-2x)?

y=sin(-2x)=-sin2x

Single increase range: balance and deficiency blind from 2+2k

The monotonic reduction interval of y=2sin(2x- 3) is .

2k + 2 2x- 3 2k +3 2 can be solved to obtain the value of x.

kπ+5π/12≤x≤kπ+11π/12

The monotonic reduction interval of the original function is.

k +5 12, k +11 Qi Tie Gaze 12].

π/4+kπ,3π/4+kπ)(k∈z)

For the function y=f(x)=sin2x, when the slag envy 2x ( 2+2k ,3 2+2k )(k z), f(x) decreases monotonically, and when x ( 4+k ,3 4+k )(k z) is solved, f(x) decreases monotonically, that is, the monotonically decreasing interval of the function y=sin2x is ( 4+k ,3 4+k )(k z).

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Original=lgcos2x=

According to the composite function, the same increases and decreases.

Find the subtraction interval of cos2x in (0,1).

2kπ<=2x

2kπ+π/2

kπ<=x

Let f(x)=|sinx|+|cosx|，f（x+π/2）=|sinx|+|cosx|, knowing f(x)=f(x+ 2), so the period is 2

Therefore, only the [0, 2] image needs to be drawn.

1. When x (0, 4), sinx and cosx are both greater than 0; In this case, f(x)=|sinx|+|cosx|=sinx+cosx=√2sin（x+π/4）

So f(x) can be drawn in x (0, 4) and is monotonically increasing.

2. When x ( 4, 2), sinx>0, cosx<0, then f(x)=|sinx|+|cosx|=sinx-cosx=√2sin（x-π/4）

So f(x) can be drawn at x (4, 2), which is monotonically decreasing.

The binding period knows f(x)=|sinx|+|cosx|Monotonically increasing at [(k) 2, (k) 2+ 4] kz, and decreasing monotonically at [(k) 2+ 4, (k2)+2]kz.

Note: If you are a high school student, it is best to remember about the function f(x)=|sinx|+|cosx|The conclusion is very common in the third year of high school].

Graphically the answer should be the quickest, y=|sinx| +cosx|It can be seen as forming like this:

"Mirror" the negative half of sinx, halving the period to 180° or radians

Then the negative half of the cosx is "mirrored", and the period is halved to 180° or radian

Add the above two periodic functions that are 90° wrong, and of course, the period is halved to 90° or radians 2

That is to say, y=|sinx| +cosx|The period is 90°, and of course the monotonic reduction interval is half of 90° (you will find that it is the second half of the picture):

45°,90°] k 90° k is an integer.

Or: [ 4, 2] k2 ===> :1 2k) 4,(1 k) 2] k2

Added:1 y=|sinx| +cosx|The period is 90°

2.The maximum value is 2

3.The minimum value is 1

It is easy to know that the period of the above function is 1 2 vultures, and from the definition of monotonicity and the formula of the sum and difference product of sine and cosine, the monotonic reduction interval of this function is [(n+1 4)vulture, (n+1 2)vulture], and n is an integer.

with f(x)=y2=1+|sin2x|is the same for monotonic intervals.

k 2 + 4, k 2 + 2] k is an integer.