Question 1: Well, Y=SINX is the basic form of sine function, and its minimum positive period is 2π, but many times the function we see is not so simple.

For example, the function Y=SIN(2X+3/π) has a minimum positive period T=2π/2=π because its w=2.

Here we can use this method to judge the minimum positive period of trigonometric function, that is, put out the numbers in brackets after s in and cos respectively. For example, Y=SINX can be regarded as Y=SIN(X), then its w= 1, and so on.

Question 2: According to the translation theory of trigonometric functions, when sinx becomes sin(2x), all the points on the function image need to be compressed to the original 1/2 times. In other words, if sinx becomes sin( 1/2x), all the points on the function image need to be stretched to the original 2 times.