The domain of does not exist at , for is an integer.

The ends of every period approaches to either positive or negative infinity. Notice that for this problem, the entire graph shifts to the right units. This means that the asymptotes would also shift right by the same distance.

The asymptotes will exist at:

Therefore, the domain of will exist anywhere EXCEPT:

Based on this data, we can make a little triangle that looks like:

This is because .

Now, this means that must equal . (Recall that the cosine function is negative in the second quadrant.) Now, we are looking for:

or . This is the cosine of a reference angle of:

Looking at our little triangle above, we can see that the cosine of is .

Based on this data, we can make a little triangle that looks like:

This is because .

Now, this means that must equal . (Recall that the cosine function is negative in the second quadrant.) Now, we are looking for:

or . This is the cosine of a reference angle of:

Looking at our little triangle above, we can see that the cosine of is .

Looking at this form of a sine function:

We can draw the following conclusions:

• because the amplitude is specified as .
• because of the specified period of since .
• because the problem specifies there is no phase shift.
• because the -intercept of a sine function with no phase shift is .

Bearing these in mind, is the only function that fits all four of those.

Cotθ can be written as cosθ/sinθ, which results in sinθ + cos2θ/sinθ.

Combining to get a single fraction results in (sin2θ + cos2θ)/sinθ.

Knowing that sin2θ + cos2θ = 1, we get 1/sinθ, which can be written as cscθ.

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 .

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.

To find the period of Sine and Cosine functions you use the formula:
where comes from . Looking at our formula you see b is 4 so

Begin by drawing out this scenario using a little right triangle:

We know that the cosine of an angle is equal to the ratio of the side adjacent to that angle to the hypotenuse of the triangle. Thus, for our triangle, we know:

Using your calculator, solve for :

This is . Now, take the decimal portion in order to find the number of inches involved.

Thus, rounded, your answer is feet and inches.

Begin by drawing out this scenario using a little right triangle:

We know that the cosine of an angle is equal to the ratio of the side adjacent to that angle to the hypotenuse of the triangle. Thus, for our triangle, we know:

Using your calculator, solve for :

This is . Now, take the decimal portion in order to find the number of inches involved.

Thus, rounded, your answer is feet and inches.