Higher trigonometric function y 3 sin 2 x 3

The maximum value is 3 2x- 3 = 2+2k

Get x=5 12+k

The minimum value is -3 2x- 3=- 2+2k to get x=- 12+k

k is an integer.

Let (2x- 3) = a

y=3sin(2x-π/3)

At 3sinamax, a= 2+2k (k z), so at this point x {x|x=k + 12 k z} minimum a=- 2+2k (k z).

So x {x|x=k +- 12 k z} max is 3, i.e. 3*sina.

The minimum value is -3, which is the minimum value of 3*sina.

n is an integer. The maximum value is 3

In this case, 2x- 3=2n + =n +5 12 [n is an integer] The minimum value is -3

In this case, 2x- 3=2n *=n -1 12 [n is an integer].

The maximum value of y is 3 and the minimum value is -3

When 2x- 3=2k+2, the corresponding maximum value is 3, and x=k +5 12, k=0, 1, 2, 3......2x- 3=2k +3 2, corresponding to the minimum value of -3, at this time, x=k +11 12, k=0, 1, 2, 3......

Maximum3 Minimum -3 x set: Let 2x- 3=2 +k solve it yourself.

Summary. 6xcos (3x square).

y=sin(3x) then y =

6xcos (3x square).

y=xsin2x, then dy=

One less was written.

Plus it's fine.

Definite integral symbol.

cosx is a primitive function of f(x) in the interval i, then f(x)=sinxy=lnsinx, then y =

cosx/sinx

No, there is no smack. y=sin(3x) then y =

6xcos(3x²)

Periodicity: The period of the function t= . 2.

Symmetry: This function has the symmetry of an even function, i.e., y(x)=y(-x).

trigonometric function of y=2sin x.

The period of the function is t= . then repentance 2Symmetry:

This function has the symmetry of an even function, i.e., y(x)=y(-x).

3.Monotonicity: The function increases monotonically on the interval [0, ] and decreases monotonically on the interval [ ,2 ]. 4.Parity argument: This function has the odd-even dispersion of odd functions, i.e., y(-x)=-y(x).

New cycle? Dear, yes.

Not 4 ? There is another algorithm, this sinusoidal function y=2sin( x) can be obtained by the following steps: amplitude:

Since the absolute value of the number 2 in y=2sin(x) is imitation sock 2, the amplitude is 2. Period: The period of the sinusoidal function can be expressed as t=2 where is the angular frequency.

And y=2sin(x), the angular frequency is 1 2, so the period t=2 (1 2)=4. Phase angle: y=2sin(x), the phase angle is 0 because sin(0)=0.

To sum up, the trigonometric function of y=2sin(x) is: the amplitude is 2, the period is 4, and the phase angle is 0.

Yes of the pro 4

The method is as follows, please comma circle for reference:

If there is help from the landslide, please celebrate.

Summary. y’=6xcos（3x²+1）

Let +y=sin(3x +1), and + find +y

y’=6xcos（3x²+1）

Because y=sin(3x +1), y = cos(3x +1) (3x +1)'=cos(3x resells+1) 6x=6xcos(3x +1), so y'=6xcos(3x +1).

Because y=sin(3x +1), y = cos(3x +1) (3x +1)'=cos(3x resells+1) 6x=6xcos(3x +1), so y'=6xcos(3x +1).

3sinx+2e×-x+c

The rest of the problems need to be upgraded.

1 substituting x=0, 2, ,,3 2,2 into y, and using these five points to make a graph;

2. There is no unique way to describe the change, which can be clearly expressed in the following order: x-direction translation, x-direction contraction, y-direction expansion, y-direction translation;

In this example, move 2 units to the right, expand by 1x in the X direction and 2 times in the Y direction;

3 amplitude = maximum displacement from equilibrium position = 3, period = distance between two adjacent peaks (valleys) = 4, initial phase = vibration ** image and y-axis focal ordinate = 3 2 2

4. The axis of symmetry is the abscissa corresponding to the peak and the valley = 3 2 2, and the center of symmetry is the equilibrium position = 2 2

Answer: It's y=3sin2x, let's ask for it first.

Axis of symmetry. 2x=k + Yunda 2

Namely. x=kπ/2+π/4,k∈z

The axis of symmetry to the right of the y-axis is x=4

Rounds. Translate the image of y=3sin2x to the left by 4 units, and the axis of symmetry next to the image is the y-axis, a=4

You need to have a good grasp of the chain resistance definition of the function.

x is the independent variable, and y is the function that calls back about x.

You can add a parameter and you'll get it.

Let u=2x+x 3

y=3sin(2x+x/3)=sinu

This makes it easy to understand.

y=-3sin(2x-π/4)

Increasing the interval. That is, find the subtraction interval of y=3sin(2x-4).

2kπ+π2≤2x-π/4≤

2kπ+3π/2

2kπ+3π/4≤2x≤

2kπ+7π/4

kπ+3π/8≤x≤

kπ+7π/8

Increase interval [k +3 8, k +7 8], k z minus interval. That is, the increase interval of y=3sin(2x- 4) is obtained.

2kπ-π2≤2x-π/4≤

2kπ+π2

2kπ-π4≤2x≤

2kπ+3π/4

kπ-π8≤x≤

kπ+3π/8

The increase interval [k - 8, k + 3 8], k z(2) is subtracted by (1).

2x-4=2k+2, i.e. x=k+3 8, y has a minimum value of -3 so. The minimum value of y is -3, which is the set of x.

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2) Move the image of y=sinx to the right flat stool by 4 units to get y=sin(x- 4);

and then elongate to 2 times of the original coarse qi to obtain y=sin(1 2x- 4);

Finally, it is lengthened to 3 times the original length, and y=3sin(1 2x- 4);

3) Amplitude 6, period 4, primary phase - 4

4) Axis of Symmetry Equation 1 2

x- 4=k + 2, k z, and solve x to obtain.

Center of Symmetry 1 2

x0- 4=k, k z, solve x0 to get, (x0,0) a bit: ok blog space.