ACT Math - How to find the domain of the cosine

What is the domain of the function ?

$(-\infty, \infty )$

$(-\infty, 1]$

$[-1, \infty)$

$[-\pi, \pi]$

Explanation

The domain of a function refers to all possible values of for which an answer can be obtained. Cosine, as a function, cycles endlessly between and (subject to modifiers of the amplitude). Because there is no real number value that can be inserted into in this case which does not produce a value between and , the domain of cosine is effectively infinite.

Given a function $y=2cos(\theta)+6$ , what is a valid domain?

$(-\infty, \infty)$

$(0,\infty)$

$[0,\infty)$

Explanation

The function $y=2cos(\theta)+6$ is related to the parent function $y=cos(\theta)$ .

The domain of the parent function is $(-\infty,\infty)$ . The values and will not affect the domain of the curve.

The answer is $(-\infty,\infty)$ .

What is the domain of the function ?

$(-\infty, \infty)$

$(-\infty, 7]$

$(-\infty +7, \infty +7)$

$[-7, \infty)$

Explanation

Note that adding to the end of the equation changes nothing with respect to domain, as there is no such thing as "infinity plus seven", nor "negative infinity plus seven". The function is still infinite in domain even when shifted up units.

What is the domain of the function ?

$(-\infty, infty)$

$(-24\infty, 24\infty)$

$[-24\pi, 24\pi]$

Explanation

Note that in this case, neither the nor the on the outside affect the domain of the function. They do affect the amplitude, which means the value for range will change, but there is no such thing as "three times infinity" nor "three times negative infinity", so the effective domain remains infinite.