📚 Topic Summary
The cosine function, written as $y = \cos x$, is a fundamental trigonometric function. Its graph is a wave that oscillates between -1 and 1. Key features include its amplitude (the height of the wave), period (the length of one complete cycle), x-intercepts (where the graph crosses the x-axis), y-intercept (where the graph crosses the y-axis), maximum points (peaks), and minimum points (valleys). Understanding these features is essential for analyzing periodic phenomena.
🧮 Part A: Vocabulary
Match the term with its definition:
| Term |
Definition |
| 1. Amplitude |
A. The length of one complete cycle of the wave. |
| 2. Period |
B. The value of $x$ where the graph crosses the x-axis. |
| 3. X-intercept |
C. The value of $x$ where the graph crosses the y-axis. |
| 4. Y-intercept |
D. The maximum distance from the midline of the wave. |
| 5. Maximum |
E. The highest point on the graph. |
(Answers: 1-D, 2-A, 3-B, 4-C, 5-E)
✍️ Part B: Fill in the Blanks
The cosine function, $y = \cos x$, has a maximum value of ___. Its minimum value is ___. The graph repeats itself every ___ radians. The cosine function is an ___ function, meaning it is symmetric about the y-axis. The y-intercept of the graph is at the point (0, ___).
(Answers: 1, -1, $2\pi$, even, 1)
🤔 Part C: Critical Thinking
Explain how changing the equation to $y = 2\cos x$ affects the graph of the cosine function.