# Examples of applications of sine function images

### How do you make an image of a sine type function?

Step 1:Using the commutative method, make t=2x, then the far function becomes sin(t)

Step 2:Make an image of the function of sin(t) [that is, in some sense, sin(x)] They are just different substrates but the meaning is the same, except that this image is not equivalent to x in the question

Step 3. Change the transverse parameter of sin(t) based on t=2x. This simply means shrinking all the key points by 1/2, which means that the difference between the sin2x image and the sinx image is that it is compressed by 1/2

Expanded:

The sinx function, or sine function, is a type of trigonometric function. The sine function is a type of trigonometric function. For any real number x corresponds to a unique angle (equal to this real number in the radian system), which in turn corresponds to the uniquely determined value sinx of the sine, so that for any real number x there is a uniquely determined value sinx to which it corresponds, and a function built according to this law of correspondences, denoted y=sinx, is called the sine function.

Sinusoidal function analytic formula: y=Asin(ωx+φ)+b

The effect of each constant value on the image of the function:

φ: determines the position of the waveform in relation to the X-axis or the distance of transverse movement (left-added right-subtracted)

ω: determines the period (the smallest positive period T=2π/∣ω∣)

A: determines the peak value (i.e., the number of times of the vertical stretching and compression)

A: determines the peak value (i.e., the number of times of vertical stretching and compression)

A: determines the value of the peak value. Compression times)

b: indicates the position of the waveform in the Y-axis or the longitudinal movement distance (upward and downward)

Method of graphing using the “five-point method” of graphing

“Five-point graphing method” means that when X is taken as 0, π/2, π, π, π, π, π, π, π, π, π, π and π, respectively, the waveform is drawn as a single point.

“Five-point graphing” means taking the value of y when X is 0, π/2, π, 3π/2, and 2π respectively.

### Engineering Applications of the Sine Function

A sine wave is a signal with the most homogeneous frequency components, named for the mathematical sinusoidal curve that is the waveform of this signal. Any complex signal – such as a musical signal – can be viewed as a composite of many, many sine waves of different frequencies and sizes.

We can set up a function y=sinX, and when X is taken to be 0, 30, 60, 90, 120, 150, 180 (in degrees), the corresponding values of Y are 0, 0.5, 0.8660, 1, 0.8660, 0.5, 0. Plotting the corresponding points in a coordinate system gives us an image of a sine wave. The image is characterized by periodic changes, for example, when X=0, Y=0, and when X=180, Y=0. If X takes the value [180~360], then we can see that the image is exactly the opposite of the original (in the fourth quadrant). That’s the image of a sine wave.

I hope I can help clear your doubts.

### What does the image of sinx look like?

The image of y = sinx is called a sinusoidal curve with T = 2 Woods as the minimum positive period and x two (k ten 1/2) Woods 〈k∈z） as the axis of symmetry. The function y = sinx is a sinusoidal function, and the image of the function is a sinusoidal curve, the curve is an image with the origin as the center of symmetry, located between the parallel lines Y = -1 and y = 1, and it is the image of a periodic function with a period of 2 Woods, which is in the shape of a wavy line. Y=sinx is an odd function, so its image is symmetric about the origin, and the line perpendicular to the x-axis past the highest point is its axis of symmetry.

Images and Properties of Sine Type Functions

The sine function is an odd function, and the periods of sine functions are all 2π. The sine function y=sinx, the sine function is monotonically increasing on [-π/2+2kπ, π/2+2kπ] and monotonically decreasing on [π/2+2kπ, 3π/2+2kπ]. The sine function is symmetric about the x = π/2 + 2kπ axis and centrosymmetric about (kπ, 0).

### Properties of Sine Trigonometry

Sine trigonometry is generally used in solving related angle-related problems, such as solving triangles and quadrilaterals. It is also applied in real life, in short, it may be used in any problem involving angles.

Some expressions involving trigonometric functions:

In triangle ABC the sides corresponding to its angles are a,b,c. Use S△ABC to represent the area of triangle ABC,

then there are

①S△ABC=1/2*b*c*sin∠A=1/2*a*b*sin∠C=1/2*a*c*sin∠B. sin∠B.

②a/sin∠A=b/sin∠B=c/sin∠C.

③(sin∠A)^2+(cos∠A)^2=1.

If it’s an acute triangle, then there are also the following equations (in the case of an obtuse angle though the corresponding cos value is negative)

④a^2+b^- 2abcos∠C=c^2

Sine trigonometric images of life application examples

For example, the interface at the right-angled bend, if you use two sheets of tin made of round tubes, and with two trees to meet perpendicularly, then the tangent line at the interface of the tin is a part of it, and the only way to ensure that this splicing thicker is to ensure that it is perpendicularly connected.