Graph the function and identify the key points on one full period. 1 y= sin x 3 To draw the graph, plot all points corresponding to the relative minima, relative maxima, and x-intercepts within one cycle. Then click o -1 2T V -Bla X
Graph the function and identify the key points on one full period. 1 y= sin x 3 To draw the graph, plot all points corresponding to the relative minima, relative maxima, and x-intercepts within one cycle. Then click o -1 2T V -Bla X
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
![### Graphing the Function: \( y = \frac{1}{3} \sin(x) \)
#### Instructions
**Graph the function and identify the key points on one full period:**
\[ y = \frac{1}{3} \sin(x) \]
**Step-by-Step Guide:**
1. **Graph the Function:**
To draw the graph, you need to plot all points corresponding to the relative minima, relative maxima, and x-intercepts within one cycle. Then, connect these points smoothly to form the graph.
2. **Understanding Key Points:**
- **Relative Maxima**: The highest point within a cycle.
- **Relative Minima**: The lowest point within a cycle.
- **X-intercepts**: Points where the graph crosses the x-axis.
3. **Using the Graphing Tools:**
On the onscreen graphing interface provided:
- Use the point plotting tool to mark the specific key points.
- Use the curve drawing tool to connect these key points smoothly.
#### Graph Explanation:
The graphing interface shows a coordinate plane with a grid, labeled with the x and y axes. The x-axis has intervals and labels indicating \(\frac{\pi}{2}\), \(\pi\), \(\frac{3\pi}{2}\), and \(2\pi\). These points correspond to key positions in the periodic cycle of the sine function:
- **At \(x = 0\)**: The sine function \( \sin(x) = 0 \), so \( y = 0 \).
- **At \(x = \frac{\pi}{2}\)**: The sine function reaches its maximum \( \sin \left( \frac{\pi}{2} \right) = 1 \), and \( y = \frac{1}{3} \).
- **At \(x = \pi\)**: The sine function returns to zero \( \sin(\pi) = 0 \), so \( y = 0 \).
- **At \(x = \frac{3\pi}{2}\)**: The sine function reaches its minimum \( \sin \left( \frac{3\pi}{2} \right) = -1 \), and \( y = -\frac{1}{3} \).
- **At \(x = 2\pi\)**: The sine function completes its period and returns to zero \(](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd9ae2b74-0627-461f-a855-f05238f3c436%2F1e5f22f7-2270-4b84-9949-034b841baacb%2Fmcnxpr3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Graphing the Function: \( y = \frac{1}{3} \sin(x) \)
#### Instructions
**Graph the function and identify the key points on one full period:**
\[ y = \frac{1}{3} \sin(x) \]
**Step-by-Step Guide:**
1. **Graph the Function:**
To draw the graph, you need to plot all points corresponding to the relative minima, relative maxima, and x-intercepts within one cycle. Then, connect these points smoothly to form the graph.
2. **Understanding Key Points:**
- **Relative Maxima**: The highest point within a cycle.
- **Relative Minima**: The lowest point within a cycle.
- **X-intercepts**: Points where the graph crosses the x-axis.
3. **Using the Graphing Tools:**
On the onscreen graphing interface provided:
- Use the point plotting tool to mark the specific key points.
- Use the curve drawing tool to connect these key points smoothly.
#### Graph Explanation:
The graphing interface shows a coordinate plane with a grid, labeled with the x and y axes. The x-axis has intervals and labels indicating \(\frac{\pi}{2}\), \(\pi\), \(\frac{3\pi}{2}\), and \(2\pi\). These points correspond to key positions in the periodic cycle of the sine function:
- **At \(x = 0\)**: The sine function \( \sin(x) = 0 \), so \( y = 0 \).
- **At \(x = \frac{\pi}{2}\)**: The sine function reaches its maximum \( \sin \left( \frac{\pi}{2} \right) = 1 \), and \( y = \frac{1}{3} \).
- **At \(x = \pi\)**: The sine function returns to zero \( \sin(\pi) = 0 \), so \( y = 0 \).
- **At \(x = \frac{3\pi}{2}\)**: The sine function reaches its minimum \( \sin \left( \frac{3\pi}{2} \right) = -1 \), and \( y = -\frac{1}{3} \).
- **At \(x = 2\pi\)**: The sine function completes its period and returns to zero \(
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