### All High School Math Resources

## Example Questions

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

What is the period of

?

**Possible Answers:**

**Correct answer:**

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 #1842 : High School Math

What is the amplitude of ?

**Possible Answers:**

**Correct answer:**

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

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

What is the local maximum of between and ?

**Possible Answers:**

**Correct answer:**

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 #2 : Understanding Period And Amplitude

Which of these functions has the greatest amplitude?

**Possible Answers:**

All of these have the same amplitude.

**Correct answer:**

All of these equations have an amplitude of one except for . The amplitude is dictated by the co-efficient of the trigonometric function. In this case, all of the other functions have a coefficient of one, while the odd one out, and therefore our correct answer, has a coefficient of .

### All High School Math Resources

### Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: