# ACT Math : How to find the domain of the cosine

## Example Questions

### Example Question #1 : How To Find The Domain Of The Cosine

What is the domain of ?

Possible Answers:

Does not exist.

Correct answer:

Explanation:

The domain of a function is referring to the x values that can be plugged into the function and produce a value.

The domain of the parent function  has a domain from negative infinity to positive infinity.

The  term only shifts the function down three units, which will not affect the domain of the cosine graph.

Therefore, the answer is .

### Example Question #2 : How To Find The Domain Of The Cosine

Given a function , what is a valid domain?

Possible Answers:

Correct answer:

Explanation:

The function  is related to the parent function .

The domain of the parent function is .  The values  and  will not affect the domain of the curve.

The answer is .

### Example Question #1 : How To Find The Domain Of The Cosine

What is the domain of the following trigonometric equation:

Possible Answers:

Correct answer:

Explanation:

For sine and cosine, they can take any for , thus the domain is all real numbers or:

### Example Question #22 : Cosine

What is the domain of the function  ?

Possible Answers:

Correct answer:

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.

### Example Question #23 : Cosine

What is the domain of the function ?

Possible Answers:

Correct answer:

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.

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.

### Example Question #24 : Cosine

What is the domain of the function ?

Possible Answers:

Correct answer:

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.

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.