state the domain and range of the function and sketch a graph showing four periods. y = - sin²x what is the…

state the domain and range of the function and sketch a graph showing four periods. y = - sin²x what is the domain? (type your answer in interval notation.)

state the domain and range of the function and sketch a graph showing four periods. y = - sin²x what is the domain? (type your answer in interval notation.)

Answer

Explanation:

Step1: Recall domain of sine function

The function $y = \sin x$ has a domain of all real - numbers. For the function $y=-\sin^{2}x$, there are no restrictions on the values of $x$ for which the function is defined. The domain of $y = \sin x$ is $x\in(-\infty,\infty)$. Since $y =-\sin^{2}x$ is a composition and transformation of the sine function, the domain of $y =-\sin^{2}x$ is also all real numbers.

Step2: Write domain in interval notation

The set of all real numbers in interval notation is $(-\infty,\infty)$.

Answer:

$(-\infty,\infty)$