Can anyone explain the sinusoidal equation to me?

1. Images and properties of trigonometric functions.

sinx= cosx= tanx= cotx=

Define the domain x r x r

Range [-1,1] [1,1] (

Image Parity Odd Functions Even Functions Odd Functions Odd Functions.

Monotonicity Monotonic increases the interval [2k -,2k +]k z

Monotonic decreasing interval [2k +, 2k +] k z monotonically increasing interval.

2kπ-π2kπ]k∈z

Monotonic subtraction interval.

2k, 2k + k z monotonically increase the range.

k -, k +)k z monotonically decreasing interval.

kπ,kπ+πk∈z

Periodicity t=2 t=2 t= t=

Symmetry Center of Symmetry:

kπ,0) k∈z

Axis of symmetry: x=k +, k z center of symmetry:

kπ+,0)k∈z

Axis of symmetry: x=k, k z center of symmetry: (,0) center of symmetry: (0).

When the maximum value is x=2k +, y takes the maximum value of 1;

When x=2k+, y takes the minimum value of -1; When k z x=2k, y takes the maximum value of 1;

When x=2k+, y takes the minimum value of -1; k z none none.

2. Image and properties of the function y=asin(x+) (a>0, 0).

1 Image The image of the function y=asin( x+)(a>0, 0)xr can be transformed from the y=sinx image in the following order:

Phase Transformation: Move all points on the y=sinx image to the left (>0) or right (<0) in parallel ||units

Periodic transformation: Shorten (>1) or elongate (0< <1) of the abscissa of all points to their original times (the ordinate does not change).

Amplitude transformation: the ordinate of all points is elongated (a>1) or shortened (0) The purpose of studying the sinusoidal function is to reveal the internal relationship of various sinusoidal function images, but when making a simple diagram of y=asin(x+), the "five-point method" is still often used, and the method of taking these five points is: let x= x+, and take 0,, 2 from x to find the corresponding value of x

Can't send the picture? I won't.

The darkness of the shadows, slow.

Autumn is yellowed, and the memories of the vicissitudes of life are brushed away.

We drink at noon, we drink in the morning, we drink at night.

I saw rocks, clay, chalk.

It feels like a child, crammed between these legs haha.

Isn't it an image of y=sinx?

The sinusoidal curve is the image of the function y=asin( x+ )k in a Cartesian coordinate system, <>

Sinusoidal curve] 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 sign, x is the value on the x-axis of the Cartesian coordinate system, y is the value of the function corresponding to the function on the same Cartesian coordinate system, and k, and are constants (k, , r, and ≠0).

Sine curve The sine curve can be expressed as y=asin( x+ )k, which is defined as the image of the function y=asin( x+ )k on 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 y-value corresponding to the function on the same Cartesian coordinate system, k, and are constants (k, , r), 0 The sinusoidal curve is a wavy line x r is a constant intersect with the x-axis but not necessarily (0,0). a - amplitude, when the object is in a straight reciprocating motion with a trajectory in line with a sinusoidal curve, its value is 1 2 ( x+ ) phase of the stroke, the state in which the reaction variable y is located - the initial phase, the phase at x=0 k - offset, the image reflected on the coordinate system is the overall upward or downward movement of the image.

1. A sinusoidal curve is a kind of curve that comes from the proportion of sinoids in mathematical trigonometry. It is also a representation of an analog signal, as opposed to a square wave, which represents a digital signal.

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 in a Cartesian coordinate system, where sin is a sinusoidal symbol, x is the numerical value on the x-axis of the Cartesian coordinate system, y is the corresponding y value of the function in the same Cartesian coordinate system, and k, , and are constants (k, , r, and ≠0).

3. A sinusoidal curve is a wavy line. a - amplitude, when the object is in a straight reciprocating motion with a trajectory in accordance with a sinusoidal curve, its value is 1 2 of the stroke. (x+) phase, which reflects the state of the variable y.

primary phase, phase at x=0; Reflected in the coordinate system, it is the left-right movement of the image. k - the offset, which is reflected in the coordinate system as the upward or downward movement of the image. – angular velocity, which controls the sinusoidal period (the number of vibrations in a unit radian).

Summary. Hello dear, how to get the curve y=4sinx from the sinusoidal curve y=sinx, the answer is that the abscissa is unchanged, and the ordinate becomes 4 times the original.

How to get the curve from the sinusoidal curve y=sinx Hello dear, how to get the curve from the sinusoidal curve y=sinx to the curve y=4sinx, the answer is that the abscissa remains the same, and the ordinate becomes 4 times the original.

Extension, point out what steps the sinusoidal curve y=sinx goes through to get the image transformation of the sinusoidal curve y=13sin(4x- 3) function width and vertical y=asin( x+ ) [Answer] Solution: first change the abscissa of each point on the sinusoidal curve to the original 14 (the ordinate remains unchanged), and obtain the image of y=sin4x, and then translate the resulting cavity image to the right 12 units, and then change the ordinate of each point on the obtained image to the original 13 (abscissa unchanged), Obtain the image of y=13sin(4x- 3) 【Analysis】First shorten the abscissa of each point on y=sinx, then translate the obtained image to the right, and then compress the ordinate of each point on the obtained image to obtain the image of y=13sin(4x- 3).

a=(y1-y0)/2

k=(y1+y0)/2

w=2 t=2 (x1-x0)*2= x1-x0) There are many algorithms, and the simplest is to bring the coordinates in.

I haven't done math in more than ten years, oh roar, god-like uncle.

The conceptual 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 on the same Cartesian coordinate system, k, , and are constants (k, , r, and ≠0) and the sinusoidal curve is a wavy line.