state the domain and range of the function and sketch a graph showing two periods. y = cos²x what is the…

state the domain and range of the function and sketch a graph showing two periods. y = cos²x what is the domain? (type your answer in interval notation.)

state the domain and range of the function and sketch a graph showing two periods. y = cos²x what is the domain? (type your answer in interval notation.)

Answer

Explanation:

Step1: Recall cosine domain property

The function $y = \cos x$ has a domain of all real - numbers. For $y=\cos^{2}x$, since we are just squaring the output of the cosine function, there are no restrictions on the input $x$. The domain of $y = \cos x$ is $x\in(-\infty,\infty)$. Squaring it does not change the domain.

Step2: Write domain in interval notation

The interval notation for all real numbers is $(-\infty,\infty)$.

Answer:

$(-\infty,\infty)$