Graph the trigonometric function. 1 y = COs x + Plot all points corresponding to x-intercepts, minima, and maxima within one cycle. Then click on the graph-a-function button.
Graph the trigonometric function. 1 y = COs x + Plot all points corresponding to x-intercepts, minima, and maxima within one cycle. Then click on the graph-a-function button.
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°.
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![### Graphing a Trigonometric Function
**Problem Statement:**
Graph the trigonometric function.
\[ y = \frac{1}{2} \cos \left( x + \frac{\pi}{2} \right) \]
Plot all points corresponding to x-intercepts, minima, and maxima within one cycle. Then click on the graph-a-function button.
**Instructions:**
1. Examine the given trigonometric function \( y = \frac{1}{2} \cos \left( x + \frac{\pi}{2} \right) \).
2. Identify and plot the x-intercepts, the minimum point, and the maximum point of the function within one cycle.
3. Use the graph-a-function tools to sketch the function appropriately.
**Graph Explanation:**
- The graph provided is a coordinate plane marked with an x-axis and y-axis.
- The x-axis is scaled in units from \(-\pi\) to \(\pi\).
- The y-axis is scaled from -3 to 3.
- Tools for graphing include an eraser, plotting tool, free-draw tool, and grid adjuster.
**User Interface:**
- Below the graph, there are two buttons: "I Don't Know" and "Submit" for user interaction.
**Interactive Tools:**
- **Pencil Icon:** For plotting points.
- **Eraser Icon:** To remove plotted points.
- **Free-Draw Tool:** To sketch curves or lines.
- **Grid Adjuster:** To toggle or adjust the graph grid.
- **Reset Button:** Clears all plotted points and drawings.
- **Help Icon:** Provides additional instructions or help.
Remember to correctly identify and plot all the critical points of the function within one cycle to accurately represent the trigonometric function on the graph. The function \( y \) represents the cosine wave, adjusted by a phase shift of \( \frac{\pi}{2} \) to the left and scaled by \( \frac{1}{2} \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48223f7c-9601-4bef-a109-141dadd72801%2F6a5d7d97-9068-4e3e-8685-12f2e7457590%2F8amkw2_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Graphing a Trigonometric Function
**Problem Statement:**
Graph the trigonometric function.
\[ y = \frac{1}{2} \cos \left( x + \frac{\pi}{2} \right) \]
Plot all points corresponding to x-intercepts, minima, and maxima within one cycle. Then click on the graph-a-function button.
**Instructions:**
1. Examine the given trigonometric function \( y = \frac{1}{2} \cos \left( x + \frac{\pi}{2} \right) \).
2. Identify and plot the x-intercepts, the minimum point, and the maximum point of the function within one cycle.
3. Use the graph-a-function tools to sketch the function appropriately.
**Graph Explanation:**
- The graph provided is a coordinate plane marked with an x-axis and y-axis.
- The x-axis is scaled in units from \(-\pi\) to \(\pi\).
- The y-axis is scaled from -3 to 3.
- Tools for graphing include an eraser, plotting tool, free-draw tool, and grid adjuster.
**User Interface:**
- Below the graph, there are two buttons: "I Don't Know" and "Submit" for user interaction.
**Interactive Tools:**
- **Pencil Icon:** For plotting points.
- **Eraser Icon:** To remove plotted points.
- **Free-Draw Tool:** To sketch curves or lines.
- **Grid Adjuster:** To toggle or adjust the graph grid.
- **Reset Button:** Clears all plotted points and drawings.
- **Help Icon:** Provides additional instructions or help.
Remember to correctly identify and plot all the critical points of the function within one cycle to accurately represent the trigonometric function on the graph. The function \( y \) represents the cosine wave, adjusted by a phase shift of \( \frac{\pi}{2} \) to the left and scaled by \( \frac{1}{2} \).
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