# High School Math : Trigonometric Graphs

## Example Questions

### Example Question #1 : Understanding Period And Amplitude

What is the period of

?

Explanation:

The period for  is . However, if a number is multiplied by , you divide the period  by what is being multiplied by . Here,  is being multiplied by    equals

### Example Question #2 : Understanding Period And Amplitude

What is the amplitude of ?

Explanation:

The amplitude of a wave function like  is always going to be the coefficient of the function. In this case, that is .

### Example Question #3 : Understanding Period And Amplitude

What is the local maximum of  between  and ?

Explanation:

The fastest way to solve this problem is to graph it and observe the answer. However, the other option is to think of this equation in terms of period.

When the coefficient of the variable increases, the frequency increases and the period decreases by that rate.

Since our equation is , our period will be  the normal period of a  wave. Since only the period is changing, the amplitude is not. Therefore the amplitude (the highest and lowest points) of  will be the same as that of . The amplitude of a sine wave is , so the amplitude of  will also be .

Therefore, our maximum will be .

### Example Question #8 : Period And Amplitude

Which of the given functions has the greatest amplitude?