Find the domain and domain of the function y = 3sin (x + n \ 6) -2.

A function is given y = 3 * sin (x + п / 6) – 2.

Scope – all valid values of the variable x.

The value of the variable X is here determined by the domain of the function y = sinx – the entire number axis. Since here the number п / 6 is added to the argument, the values of the argument do not change.

The sine value of a certain angle (x + п / 6) can be a number from -1 to 1. Let’s write this:

-1 <sin (x + п / 6) <1;

Multiply all parts of the inequality by 3:

-3 <3 * sin (x + п / 6) <3;

Add -2 to all parts of the inequality:

-5 <3 * sin (x + п / 6) + 2 <1.

The function range is all numbers from -5 to 1.