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Shorten the mathematical cycle
( 1)

y=sinx

First, shift π/3 units to the left.

Y=sin(x+π/3) is obtained, and then the abscissa of all points on the image is changed to the original 1/2 times.

Get y=sin(2x+π/3)

Its period is π.

(2)y=sin(2x+π/3) is written as y=sin2(x+π/6)

And y=sin(2x+π/4) can be written as y=sin2(x+π/8).

So just put y=sin2(x+π/6)

Y=sin2(x+π/8) moves π/24 units to the right with a period of π.

Addition and subtraction of independent variables

Left plus right MINUS

Function value addition and subtraction

add, subtract, multiply and divide

Phase change

Become a multiple of the original number.