Lesson 2
1. Lesson 2
1.5. Explore
Module 6: Sinusoidal Functions
Explore
Throughout previous math courses and in this course, you have learned about different functions: linear, quadratic, polynomial, and rational. In Try This 1 you were introduced to the sine function and discovered that the graph looks like the following.
A similar function to the sine function is the cosine function, which is shown with the table of values. Notice that the sine and cosine functions have the same output values, but the inputs or x-values are offset by 90°.
| x | cos x |
| 0° | 1 |
| 30° | 0.866 |
| 60° | 0.5 |
| 90° | 0 |
| 120° | –0.5 |
| 150° | –0.866 |
| 180° | –1 |
| 210° | –0.866 |
| 240° | –0.5 |
| 270° | 0 |
| 300° | 0.5 |
| 330° | 0.866 |
| 360° | 1 |
| 390° | 0.866 |
| 420° | 0.5 |
| 450° | 0 |
| 480° | –0.5 |
| 510° | –0.866 |
| 540° | –1 |
| 570° | –0.866 |
| 600° | –0.5 |
| 630° | 0 |
| 660° | 0.5 |
| 690° | 0.866 |
| 720° | 1 |
Both the sine and cosine functions are periodic functions. A periodic function is a function that repeats itself at regular intervals.
The periodic functions you will study in this course have the following characteristics:
- The maximum and minimum are the highest and lowest points the function reaches.
- The midline is halfway between the maximum and minimum.
- The amplitude is the distance from the midline to a maximum or a minimum.
- Finally, the period is the length of one cycle of the function.
