# Case Study Design for Teaching Images of Sine Functions

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.

### What is the graphing of the sine function and the inverse sine function?

From the fact that the image of the original function and the image of its inverse function are symmetric about the one-third quadrant angle bisector: we know that the image of the sine function and the image of the inverse sine function are also symmetric about the one-third quadrant angle bisector.

Graphing: first draw the image of the function

on

, trace the image on a plate glass or transparency, and flip it over.