In right triangles, SOHCAHTOA tells us that , and we know that  and hypotenuse . Therefore, a simple substitution and some algebra gives us our answer.

 Use a calculator or reference to approximate cosine.

 Isolate the variable term.

Thus, .

In right triangles, SOHCAHTOA tells us that , and we know that  and hypotenuse . Therefore, a simple substitution and some algebra gives us our answer.

 Use a calculator or reference to approximate cosine.

 Isolate the variable term.

Thus, .

The plane itself is effectively at the top of a right triangle, with topmost angle  and hypotenuse  feet. If this is the case, then SOHCAHTOA tells us that .

Now, solve for the adjacent:

Thus, our plane's nose is approximately  feet from the runway.

Edgar is standing on top of a right triangle because the angle from the vertical ladder to the ground is 90 degrees. To solve this question, you must know SOHCAHTOA. This acronym can be broken into three parts to solve for the sine, cosine, and tangent.

In order to solve for the missing side, you need to choose the trigonometric function that includes the side you need to find and the side that you know, relative to the angle that you know. In this case, you know the hypotenuse, so you would not use the tangent function; furthermore, you are looking for the side that is adjacent to the 68-degree angle. Thus, you need the function that incorporates adjacent and hypotenuse—the cosine function.

Typically, you would use a calculator at this point to calculate the cosine function; however, based on the answer choices provided, you can stop at this point.

In right triangles, SOHCAHTOA tells us that , and we know that  and hypotenuse . Therefore, a simple substitution and some algebra gives us our answer.

 Use a calculator or reference to approximate cosine.

 Isolate the variable term.

Thus, .

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 .

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 .

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

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.

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.