For the equation, first identify the phase shift and sketch (at least) one complete cycle of the graph. The graph of y = sin x is given. y = sin ( + Phase Shift: Preview |-1/2 T/2 Зл/2
For the equation, first identify the phase shift and sketch (at least) one complete cycle of the graph. The graph of y = sin x is given. y = sin ( + Phase Shift: Preview |-1/2 T/2 Зл/2
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
![For the equation, first identify the phase shift and sketch (at least) one complete cycle of the graph. The graph of \( y = \sin x \) is given.
\[ y = \sin \left( x + \frac{\pi}{2} \right) \]
**Phase Shift:**
[Input box] [Preview button]
The graph displayed shows a sine wave that has been shifted to the left by \(\frac{\pi}{2}\) units. The graph is drawn over the interval from \(-\pi/2\) to \(2\pi\).
- **Axes and Labels:**
- The x-axis is labeled with major points at \(-\pi/2\), \(\pi/2\), \(\pi\), \(3\pi/2\), and \(2\pi\).
- The y-axis ranges from -1 to 1.
- **Graph Characteristics:**
- The sine wave starts at the peak at \((0, 1)\).
- It crosses the x-axis at \(-\pi/2\) and \(\pi/2\).
- The minimum point is at \((3\pi/2, -1)\).
You can visualize how the graph compares to the standard sine wave, \( y = \sin x \), by noticing the leftward phase shift of \(\frac{\pi}{2}\).
[Clear All button] [Draw button: sine wave curves]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42bd253a-231b-4c16-baac-6c405dc75416%2Fff138db4-6b97-4d04-8a09-7f84f7af9bf7%2F2m90gl_processed.png&w=3840&q=75)
Transcribed Image Text:For the equation, first identify the phase shift and sketch (at least) one complete cycle of the graph. The graph of \( y = \sin x \) is given.
\[ y = \sin \left( x + \frac{\pi}{2} \right) \]
**Phase Shift:**
[Input box] [Preview button]
The graph displayed shows a sine wave that has been shifted to the left by \(\frac{\pi}{2}\) units. The graph is drawn over the interval from \(-\pi/2\) to \(2\pi\).
- **Axes and Labels:**
- The x-axis is labeled with major points at \(-\pi/2\), \(\pi/2\), \(\pi\), \(3\pi/2\), and \(2\pi\).
- The y-axis ranges from -1 to 1.
- **Graph Characteristics:**
- The sine wave starts at the peak at \((0, 1)\).
- It crosses the x-axis at \(-\pi/2\) and \(\pi/2\).
- The minimum point is at \((3\pi/2, -1)\).
You can visualize how the graph compares to the standard sine wave, \( y = \sin x \), by noticing the leftward phase shift of \(\frac{\pi}{2}\).
[Clear All button] [Draw button: sine wave curves]
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