What is the axis of symmetry of a sinusoidal curve

The axis of sinusoidal symmetry is x=k + 2 and k is an integer.

Addendum: The sinusoidal curve can be expressed as y=asin(x+)k, which is defined as the image of the function y=asin(x+)k in a Cartesian coordinate system, where sin is the sinusoidal symbol, x is the value on the x-axis of the Cartesian coordinate system, y is the value of the function corresponding to the function in the same Cartesian coordinate system, and k, and are constants (k, , r, and ≠0).

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When the waveform moves, it should be noted that the amplitude a becomes larger, and the difference between the maximum and minimum values of the waveform on the y-axis becomes larger; If the amplitude a decreases, the opposite is true; When the angular velocity increases, the waveform shrinks on the x-axis (the waveform becomes compact); The angular velocity decreases, and the waveform spreads on the x-axis (the waveform becomes sparse). Another point is that if you want to move the waveform to the left or right if you want to move y=asin( x+ )) to the left, then it should be changed to this form of the formula y=asin[ (x+ ))] if you want to move the m angle to the right, it becomes y=asin[ (x+ -m)], and vice versa, if you move to the left, it becomes y=asin[ (x+ +m)].

y=k+pie 2 k=

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The sine function has the most basic common and starvation formula: y=asin(wx+) axis of symmetry(wx+)k + kz), center of symmetry(wx+)k+(kz), and solve x.

Example: y=sin(2x- 3) to find the axis of symmetry and the center of symmetry.

Axis of symmetry: 2x- 3=k + 2, x=k 2+5 12 center of symmetry: 2x- 3=k, x=k 2+ 6, center of symmetry is (k 2 + 6,0).

The axis of sinusoidal symmetry is x=k + 2 and k is an integer.

The center of symmetry of the sinusoidal function y=sinx is the intersection of the curve and the x-axis.

The center of symmetry is: (k,0).

The axis of symmetry is the value of x when the function takes the maximum value, the axis of symmetry is: x=k 2 The sinusoidal curve can be expressed as y=asin( x+ )k, which is defined as the image of the function y=asin( x+ )k on the Cartesian coordinate system, where sin is the sinusoidal symbol, x is the value on the x-axis of the Cartesian coordinate system, y is the y value corresponding to the function on the same Cartesian coordinate system, k, and are constants (k, , r and ≠0), as shown in Fig:

The sinusoidal function y = sinx center of symmetry (k,0).

The axis of symmetry is the value of x when the function obtains the maximum value, and the axis of symmetry is: x=k 2.

Mutual search Zhengliangguan information:

Let the sinusoidal dispersion function be y=sinx, and its axis of symmetry is a straight line perpendicular to the x-axis through the highest or lowest point of its image, with two periods per period, and the equation is x=k ten 2,k z. The center of symmetry is the coordinate of the intersection of the sinusoidal function and the x-axis, and its coordinates are (k, 0), and the image of the sine function is axisymmetric and centrally symmetrical.

The maximum value and zero point of the sinusoidal function: the maximum value is when x = 2k + (2), k z, y(max) = 1. The minimum value is when x = 2k + (3 2), k z and y(min) = -1.

Zero point: (k, 0)), k z.

Axis of symmetry: With respect to the straight line x=(2)+k, kz symmetry. A sinusoidal function is a type of trigonometric function.

For any real number x corresponds to a unique angle, and this angle corresponds to a uniquely determined sine value sinx, so that for any real number x there is a unique definite value sinx corresponding to it, and the function built according to this correspondence rule is expressed as y=sinx, which is called a sinusoidal function.

Define the domain

The set of real numbers r, which can be extended to the set of complex numbers c

Range

1,1] (the embodiment of the boundedness of the sinusoidal function).

Maximums and zerosMaximum: When x=2k+(2),kz,y(max)=1Minimum:When x=2k+(3 2),kz,y(min)=-1 zero point:

kπ，0)，k∈z

Symmetry

1) Axis of symmetry: about the straight line x = (2) + k, k z symmetry.

2) Center symmetry: with respect to the point (k, 0), k z symmetry.

Periodicity

Minimum positive period: 2

Parity

The odd function is this sum sensitive (its image is symmetrical with respect to the origin).

Monotonnia

On [-(2)+2k, (2)+2k], k z is the increment function.

On [(2)+2k,(3 2)+2k],k z is the shed-reducing wheel function.

The most basic formula for the sinusoidal function is: y=asin(wx+) axis of symmetry(wx+)k + kz), center of symmetry(wx+)k+(kz), and x.

Example: y=sin(2x- 3) to find the axis of symmetry and the center of symmetry.

Axis of symmetry: 2x- 3=k + 2, x=k 2+5 12 center of symmetry: 2x- 3=k, x=k 2+ 6, center of symmetry is (k 2 + 6,0).

y=sinx (sinusoidal function.

Axis of symmetry: x=k + 2(k z) center of symmetry: (k,0)(k z), axis of symmetry (axisofsymmetry) refers to an imaginary straight line in an object or figure, around which every certain angle of rotation occurs, the same parts of the object or figure are repeated, that is, the whole object or figure is restored once.

The sine formula is a description of the sine theorem.

The implicit expression of the relevant public argument is that in any flat triangle, the ratio of the sinusoids of each side to its opposite angle is equal and equal to the circumscribed circle.

diameter. The sine theorem is a fundamental theorem in trigonometry, which states that in a geometric sense, the sine formula is the sine theorem.

Sine: The axis of symmetry.

x=k + 2, and k is an integer balance.

The center of symmetry (k, 0) k is an integer.

Cosine. For this the axis of the major axes x=k where k is an integer.

The center of symmetry (k + 2,0) k is an integer.

Tangent: No axis of symmetry.

The center of symmetry (k 2,0) and the vertical k are integers.

The sine function has the most basic common and starvation formula: y=asin(wx+) axis of symmetry(wx+)k + kz), center of symmetry(wx+)k+(kz), and solve x.

Example: y=sin(2x- 3) to find the axis of symmetry and the center of symmetry.

Axis of symmetry: 2x- 3=k + 2, x=k 2+5 12 center of symmetry: 2x- 3=k, x=k 2+ 6, center of symmetry is (k 2 + 6,0).

With respect to the straight line x=(2)+k, k z is symmetrical and vertical. The sine cobridge function is a type of trigonometric function. For any real number x corresponds to a unique angle, and this angle corresponds to a definite sine value sinx in the virtual calendar, so that for any real number x there is a unique definite value sinx corresponding to it, and the function established according to this correspondence rule is expressed as y=sinx.

The most basic formula for the sinusoidal function is: y=asin(wx+) axis of symmetry(wx+)k + kz), center of symmetry(wx+)k+(kz), and x.

Example: y=sin(2x- 3) to find the axis of symmetry and the center of symmetry.

Axis of symmetry: 2x- 3=k+2, x=k2+5 12.

Center of symmetry: 2x- 3=k, x=k2+ 6, center of symmetry is (k2+ 6,0).

Sine: The axis of symmetry.

is x=k 2 and k is an integer.

Sine function. The center of symmetry of y=sinx is the intersection of the curve and the x-axis. Eyes on the cheeks.

The center of symmetry is: (k,0).

The axis of symmetry is the value of x when the function obtains the maximum value, and the axis of symmetry is: x=k 2 sinusoidal curve. It can be expressed as y=asin(x+)k, which is defined as the function y=asin(x+)k in a Cartesian coordinate system.

where sin is the positive file string symbol, x is the value on the x-axis of the Cartesian coordinate system, y is the y-value corresponding to the function on the same Cartesian coordinate system, and k, , and are constants (k, , r, and ≠0), as shown in the figure

The axis of symmetry of the sinusoidal function refers to which line the image is symmetrical about. For a sinusoidal function, it has two axes of symmetry:

Axis: The sinusoidal function y = sin(x) is based on the x-axis as the axis of symmetry. This means that points that are symmetrical above and below the x-axis have the same function value.

For example, when x = 0, y = sin(0) =0, and when x = , y = sin( )0, this indicates that the image has symmetry on the x-axis.

2.Perpendicular line: The sinusoidal function also has symmetry with respect to the perpendicular line leakage x = k (k is an integer).

This means that in each full or half period, the image of the sinusoidal function is symmetrical in the positions of the vertical line x = k and the vertical line x = k + 1 2). Specifically, when x = k, y = sin(k) 0, and when x = k + 1 2), y = sin((k + 1 2))1, which shows that the function image is symmetrical on these two vertical comma lines.

These symmetries can be used to simplify the image drawing and property analysis of sinusoidal functions. They show the repetitive and periodic properties of the sine function and can help us understand how the sine function changes across the defined domain.

The sine function takes the maximum or minimum value on the axis of symmetry, and the axis of symmetry of the sine function is:

y-axis (x=0);

All straight lines parallel to the y-axis;

All lines parallel to the x-axis.

Specifically, the axis of symmetry of the sinusoidal function sin(x) is x=k and k is an integer. This is because the sinusoidal function takes the maximum or minimum value of the circular brigade at this point. If we translate the sinusoidal function to the left or right k before the Hui Zhou Hui cavity answer period, it still takes the maximum or minimum value on the axis of symmetry.

Also, the value of the sinusoidal function on the axis of symmetry is 0 or earth 1. If we translate the sinusoidal function to the left or right for n periods, it still takes 0 or earth 1 on the axis of symmetry.

Thus, the axis of symmetry of a sinusoidal function has the y-axis and all the lines parallel to the y-axis, and all the lines parallel to the x-axis.

1.Vertical axis of symmetry: The axis of symmetry of the sinusoidal function y = sin(x) is the straight core line x = 2 or x = 2.

This means that for any x, the values of the functions of y = sin(x) and y = sin(-x) are equal.

2.Horizontal axis of symmetry: The axis of horizontal symmetry of the sinusoidal function y = sin(x) is the x-axis (y = 0). This means that when x is positive or negative, the corresponding function value is symmetrical with respect to the x-axis.

The symmetry of the sinusoidal function makes it have important applications in mathematics and physics.