W=2π/T (for tan function w=π/T), and t is the period of the function. So the larger w is, the smaller the period is and the more compact the function is.
A is the amplitude of trigonometric function, which can be considered as the stretching of the function along the Y axis. The larger a is, the greater the fluctuation of the function is. For sine function, the extreme value of the function is a.
K is the offset, the function moves to the left, K is positive, and K is negative, but note that if you really want to translate, you must convert the function into y=Asin[w(x+k/w)] and then translate, because we set a variable t=x+k/w, then the trigonometric function becomes y=Asinwt, if the range of t is 0-.
The images of cos and Tan are actually the same, but although Tan is different here, the law is actually the same.
Corresponding topic:
2tan(-x+π/4)=-2tan(x-π/4) because tan is a odd function, or it can be explained by a period, which corresponds to the above law: if y=Atan(wx+k), a =-2, w = 1, k =-π/4.
2cos(-x+π/4)=2cos(x-π/4) Because cos is an even function, it corresponds to the above law: if y=Acos(wx+k), A=2, w= 1, k=-π/4, that is, the cosx function is stretched vertically twice.
If you really want to draw a picture, it won't be so complicated, just like the five-point drawing method upstairs, because the period and waveform are known, cos and sin functions are 2π, and tan is π, so take the known point as an example, and let the part of wx+k in function brackets be equal to: 0, π/6, π/4, π/3, π.