# SAT II Math II : Graphing Trigonometric Functions

## Example Questions

### Example Question #1 : Graphing Trigonometric Functions

Give the amplitude of the graph of the function

Possible Answers:

Correct answer:

Explanation:

The amplitude of the graph of a sine function  is . Here, , so this is the amplitude.

### Example Question #1 : Graphing Trigonometric Functions

Which of these functions has a graph with amplitude 4?

Possible Answers:

Correct answer:

Explanation:

The functions in each of the choices take the form of a cosine function

.

The graph of a cosine function in this form has amplitude . Therefore, for this function to have amplitude 4, . Of the five choices, only

matches this description.

### Example Question #3 : Graphing Trigonometric Functions

Which of these functions has a graph with amplitude  ?

Possible Answers:

Correct answer:

Explanation:

The functions in each of the choices take the form of a sine function

.

The graph of a sine function in this form has amplitude . Therefore, for this function to have amplitude 4, . Of the five choices, only

matches this description.

### Example Question #4 : Graphing Trigonometric Functions

Which of the following sine functions has a graph with period of 7?

Possible Answers:

Correct answer:

Explanation:

The period of the graph of a sine function , is , or .

Therefore, we solve for :

The correct choice is therefore .

### Example Question #1081 : Pre Calculus

Which of the given functions has the greatest amplitude?

Possible Answers:

Correct answer:

Explanation:

The amplitude of a function is the amount by which the graph of the function travels above and below its midline. When graphing a sine function, the value of the amplitude is equivalent to the value of the coefficient of the sine. Similarly, the coefficient associated with the x-value is related to the function's period. The largest coefficient associated with the sine in the provided functions is 2; therefore the correct answer is .

The amplitude is dictated by the coefficient of the trigonometric function. In this case, all of the other functions have a coefficient of one or one-half.