Use the method of adding y-coordinates to graph the following function for 0sxs2x. y= -5 sin x + sin 2x Choose the correct graph below. OD. OA. O B Oc. AY
Use the method of adding y-coordinates to graph the following function for 0sxs2x. y= -5 sin x + sin 2x Choose the correct graph below. OD. OA. O B Oc. AY
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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17
![**Graphing a Trigonometric Function**
**Task:** Use the method of adding y-coordinates to graph the following function for \(0 \leq x \leq 2\pi\):
\[ y = -5 \sin x + \sin 2x \]
**Instructions:** Choose the correct graph from the options below.
**Graph Options:**
- **Option A:**
- The graph shows a sinusoidal curve starting from the origin. It has peaks and troughs with the x-axis crossing points having varying intervals.
- **Option B:**
- The graph displays a sinusoidal wave with broader crests and troughs. It has two complete wave cycles across the interval from \(0\) to \(2\pi\).
- **Option C:**
- The graph is mostly flat with slight oscillations, notably not touching the higher values on the y-axis. It shows minor amplitude variations over the entire \(0\) to \(2\pi\) range.
- **Option D:**
- Shows a wave with a single major peak and a deep trough, bearing fewer oscillations within one complete cycle across \(0\) to \(2\pi\).
**Analysis:**
- The given function is composed of two sinusoidal functions: a single sine wave with a modified amplitude, \(-5 \sin x\), and another wave with a double frequency, \(\sin 2x\).
- Understanding phase and amplitude changes is crucial to identifying the correct graph.
**Note:** Evaluate each graph to see which fits the described behavior of the function in the specified interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9fe330d6-ed92-43b3-9547-c6e2b1ed5b0a%2Fe79b4f17-d045-4561-8d84-ffd66d2e951e%2Fkcfraag_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Graphing a Trigonometric Function**
**Task:** Use the method of adding y-coordinates to graph the following function for \(0 \leq x \leq 2\pi\):
\[ y = -5 \sin x + \sin 2x \]
**Instructions:** Choose the correct graph from the options below.
**Graph Options:**
- **Option A:**
- The graph shows a sinusoidal curve starting from the origin. It has peaks and troughs with the x-axis crossing points having varying intervals.
- **Option B:**
- The graph displays a sinusoidal wave with broader crests and troughs. It has two complete wave cycles across the interval from \(0\) to \(2\pi\).
- **Option C:**
- The graph is mostly flat with slight oscillations, notably not touching the higher values on the y-axis. It shows minor amplitude variations over the entire \(0\) to \(2\pi\) range.
- **Option D:**
- Shows a wave with a single major peak and a deep trough, bearing fewer oscillations within one complete cycle across \(0\) to \(2\pi\).
**Analysis:**
- The given function is composed of two sinusoidal functions: a single sine wave with a modified amplitude, \(-5 \sin x\), and another wave with a double frequency, \(\sin 2x\).
- Understanding phase and amplitude changes is crucial to identifying the correct graph.
**Note:** Evaluate each graph to see which fits the described behavior of the function in the specified interval.
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