Graphing the Cosine Function

Practice Problems: Graphing the Cosine Function

1. 1. What is the value of $\cos(0)$?
2. 2. What is the period of $y = \cos(x)$?
3. 3. What is the amplitude of $y = \cos(x)$?
4. 4. What is the value of $\cos(\pi)$?
5. 5. At what x-value does $y = \cos(x)$ first cross the x-axis (starting from $x = 0$)?
6. 6. What is the amplitude of $y = 5\cos(x)$?
7. 7. What is the period of $y = \cos(3x)$?
8. 8. What is the period of $y = \cos(4x)$? Express your answer as a fraction of $\pi$ (e.g., enter "pi/2" for $\frac{\pi}{2}$).
9. 9. The graph of $y = \cos(x - \frac{\pi}{4})$ is shifted in which direction compared to $y = \cos(x)$?
10. 10. What is the maximum value of $y = 2\cos(x) + 3$?
11. 11. Find the amplitude, period, and midline of $y = 4\cos(2x) + 1$.
12. 12. Describe all transformations of $y = -3\cos(x) + 2$ compared to $y = \cos(x)$.
13. 13. Find the equation of a cosine function with amplitude 2, period $\pi$, and phase shift $\frac{\pi}{6}$ to the right.
14. 14. Which equation represents a cosine function with a maximum at $(0, 5)$ and minimum at $(\pi, 1)$?
15. 15. A ferris wheel has a diameter of 40 meters and its center is 25 meters above the ground. It takes 2 minutes for one full rotation. Write a cosine function $h(t)$ for a rider's height above the ground, where $t$ is in minutes and the rider starts at the top.
16. 16. What is the minimum value of $y = -4\cos(x) + 2$?