Trigonometry : Period and Amplitude

Example Questions

Example Question #1 : Period And Amplitude

What is the amplitude in the graph of the following equation:       Explanation:

The general form for a sine equation is: The amplitude of a sine equation is the absolute value of .

Since our equation begins with , we would simplify the equation: The absolute value of would be .

Example Question #2 : Period And Amplitude

What is the amplitude of       Explanation:

Amplitude describes the distance from the middle of a periodic function to its local maximum. covers the range from -1 to 1. Thus, it covers a distance of 2 vertically. Half of this, or 1, gives us the amplitude of the function. It is often helpful to think of the amplitude of a periodic function as its "height".

Example Question #3 : Period And Amplitude

What is the amplitude of       Explanation:

The amplitude of a function describes its height from the midline to the maximum. The amplitude of the parent function, , is 1, since it goes from -1 to 1. In this case our function has been multiplied by 4. Think of the effects this multiplication has on the outputs. In , we get our maximum at , and . Here, we will get 4. The same thing happens for our minimum, at  , . Here, we get -4. Thus, by this analysis, it is clear that the amplitude is 4. In the future, remember that the number preceding the cosine function will always be its amplitude.

Example Question #1 : Period And Amplitude

What is the period of the function       Explanation:

By definition, the period of a function is the length of for which it repeats. starts at 0, continues to 1, goes back to 0, goes to -1, and then back to 0.

This complete cycle goes from to  .

Example Question #5 : Period And Amplitude

What is the period and amplitude of the following trigonometric function?       Explanation:

Recall the form of a sinusoid: or The important quantities for this question are the amplitude, given by , and period given by .

For this problem, amplitude is equal to and period is .

Example Question #6 : Period And Amplitude

What is the period of the following function?      Explanation:

The period of the standard cosine function is .

We can find the period of the given function by dividing by the coefficient in front of , which is : .

Example Question #7 : Period And Amplitude

Write the equation of sine graph with amplitude 3 and period of     None of the above Explanation:

Giving ,

where and Then,  ,

hence . .

Therefore, Example Question #8 : Period And Amplitude

Which of the given functions has the greatest amplitude?      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 . 