Find the Domain and Domain of a Function y = 3sin (x + n \ 6) -2

We have the function y = 3 * sin (x + п / 6) – 2.

Let’s find the domain and the domain of the function – all the valid values of the argument and the function itself.

Sine is a trigonometric function that is continuous on the entire numerical axis, respectively, the domain of our function is any number.

Valid values for the sine of an angle are numbers from -1 to 1. Let’s write this in the form of a double inequality.

-1 <= sin (x + п / 6) <= 1;

Multiply all parts of the inequality by 3:

-3 <= 3 * sin (x + п / 6) <= 3;

Add -2 to the parts of the inequality:

-5 <= 3 * sin (x + п / 6) – 2 <= 2.