3 sin(0 + 27) = 1 sin 0 cos O O - sin 0 2 sin 0 O sin 0 cos 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Trigonometry Practice Worksheet**
**Question 3**
Evaluate the following trigonometric identity:
\[ \sin(\theta + 2\pi) = \]
Options:
- ( ) \( \sin \theta \)
- ( ) \( \cos \theta \)
- ( ) \( -\sin \theta \)
- ( ) \( 2 \sin \theta \)
- ( ) \( \sin \theta \cos \theta \)
**Explanation:**
Use the property of sine function where adding \(2\pi\) to the angle \(\theta\) completes a full cycle:
\[ \sin(\theta + 2\pi) = \sin \theta \]
**Graph Description:**
The diagram at the top of the page shows a series of connected numbered circles ranging from 1 to 15, indicating the step or question progression of the worksheet.
---
**Question 4**
What is the period of the function \( y = \sin 4x \)?
- The typical discussion for this will involve the period transformation properties of trigonometric functions where the period \( T \) of the function \( y = \sin kx \) is given by \( T = \frac{2\pi}{k} \). For \( y = \sin 4x \), the period would be \( T = \frac{2\pi}{4} = \frac{\pi}{2} \).
For more practice and further explanations, please refer to the provided resources on trigonometric identities and transformations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41cc9bd4-14af-44e6-b895-a9cd3485fa4c%2F59a0974d-e8df-4fb9-9500-c61bdb5dbdba%2Fxwhgtm9_processed.png&w=3840&q=75)
Transcribed Image Text:**Trigonometry Practice Worksheet**
**Question 3**
Evaluate the following trigonometric identity:
\[ \sin(\theta + 2\pi) = \]
Options:
- ( ) \( \sin \theta \)
- ( ) \( \cos \theta \)
- ( ) \( -\sin \theta \)
- ( ) \( 2 \sin \theta \)
- ( ) \( \sin \theta \cos \theta \)
**Explanation:**
Use the property of sine function where adding \(2\pi\) to the angle \(\theta\) completes a full cycle:
\[ \sin(\theta + 2\pi) = \sin \theta \]
**Graph Description:**
The diagram at the top of the page shows a series of connected numbered circles ranging from 1 to 15, indicating the step or question progression of the worksheet.
---
**Question 4**
What is the period of the function \( y = \sin 4x \)?
- The typical discussion for this will involve the period transformation properties of trigonometric functions where the period \( T \) of the function \( y = \sin kx \) is given by \( T = \frac{2\pi}{k} \). For \( y = \sin 4x \), the period would be \( T = \frac{2\pi}{4} = \frac{\pi}{2} \).
For more practice and further explanations, please refer to the provided resources on trigonometric identities and transformations.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
