Y=3(x+ 1) can be changed into y=3t by t=x+ 1.

Two elements of substitution: form and the range of independent variables

The one above, if t has a range, such as 1

In trigonometric functions, finding the period with method of substitution is the above idea.

Y=sin(3x+4π), we directly change it into the function sin t through t=3x+4π.

We know that the period of sin x is 2kπ.

So sint and sin(3x+4π) are the same, and the period is determined by the trigonometric function of sin.

So 3x+4π also takes 2kπ as the period, 3x+4π=2kπ, so it is enough to solve X. When k is equal to 1, it is the minimum positive period, that is, to find the minimum positive period, so it is written as 3x+4π=2π, and it can be solved.

For example, tan(3x+4π) directly 3x+4π=π to solve x.

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The core of this kind of problem is to find the core periodic function first, and then make the block in the middle of that function (such as sin) equal to the period t of that function. Do it.