Chapter 7.1, Problem 1AYU

To determine

To calculate: The domain and range of $y=\sin x$ .

Answer to Problem 1AYU

Domain of $y=\sin x$ function is the set of all real numbers and range is $-1\le y\le 1$ .

Explanation of Solution

Given information:

The function $y=\sin x$ .

Formula used:

The domain of function is the set of inputs for which the function is real and defined.

The range of function is the domain of inverse function.

Calculation:

For any point on the unit circle that corresponds to angle $x$ shows $\sin x$ has no concern about dividing by zero, so $x$ can be any angle.

It follows that domain of sine function is the set of all real numbers.

The range of function is the set of values of the dependent variable for which a function is defined.

Sine function absolute minimum is $-1$ and absolute maximumis $1$ .

It gives idea of variation in $y$ for a function $\sin x$ .

Thus, the domain of $y=\sin x$ function is the set of all real numbers and range is $-1\le y\le 1$ .