A ship travels N36°E for 500 nautical miles. In component form, which vector represents this displacement? Picture not dewn to scale. 500 NM East O (500 tan(36°), 500 tan(54°)) O (500 cos(36"),500 sin(36°)) O (500 cos(54"), 500 sin(54°)) O (500 sin(36°), 500 cos(36°)) O (500 sin(54°), 500 cos(54')) North
A ship travels N36°E for 500 nautical miles. In component form, which vector represents this displacement? Picture not dewn to scale. 500 NM East O (500 tan(36°), 500 tan(54°)) O (500 cos(36"),500 sin(36°)) O (500 cos(54"), 500 sin(54°)) O (500 sin(36°), 500 cos(36°)) O (500 sin(54°), 500 cos(54')) North
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
![**Educational Content - Navigational Vector Illustration**
---
### Problem Statement:
A ship travels N38°E for 500 nautical miles. In component form, which vector represents this displacement?
---
### Diagram Explanation:
The diagram displayed on the left shows a vector originating from the origin of a coordinate system, representing the movement of the ship. The coordinate system is aligned with North-South and East-West axes.
- **Axes Labels**: The vertical axis is labeled "North" and the horizontal axis is labeled "East."
- **Vector**: The red arrow represents the direction and magnitude of the ship's travel. It points from the origin at an angle of 38° to the east of north (N38°E), extending up to a distance of 500 nautical miles, represented by the label "500 NM."
---
### Question Options:
Below the diagram, there are several options provided to choose from, which represent the components of the vector in terms of trigonometric functions:
1. **Option 1**:
\[
(500 \cdot \tan(36°), 500 \cdot \tan(54°))
\]
2. **Option 2**:
\[
(500 \cdot \cos(36°), 500 \cdot \sin(36°))
\]
3. **Option 3**:
\[
(500 \cdot \cos(54°), 500 \cdot \sin(54°))
\]
4. **Option 4**:
\[
(500 \cdot \sin(36°), 500 \cdot \cos(36°))
\]
5. **Option 5**:
\[
(500 \cdot \sin(54°), 500 \cdot \cos(54°))
\]
---
### Navigation Instructions:
There are navigation buttons at the bottom of the page numbered from 7 to 16, allowing users to move through the educational content. There are also additional navigation and interaction tools on a vertical toolbar to the right side of the interface including options to go back, flag, or use a calculator.
---
### Note:
To solve this problem, one must decompose the vector into its North and East components using sine and cosine functions for the given angle (38°).
---
**End of Educational Content**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26056068-ea34-4e16-9a12-19cfd54f09f4%2F956a1262-868c-4357-9842-32a109d70ed3%2Fmu6uoi9_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content - Navigational Vector Illustration**
---
### Problem Statement:
A ship travels N38°E for 500 nautical miles. In component form, which vector represents this displacement?
---
### Diagram Explanation:
The diagram displayed on the left shows a vector originating from the origin of a coordinate system, representing the movement of the ship. The coordinate system is aligned with North-South and East-West axes.
- **Axes Labels**: The vertical axis is labeled "North" and the horizontal axis is labeled "East."
- **Vector**: The red arrow represents the direction and magnitude of the ship's travel. It points from the origin at an angle of 38° to the east of north (N38°E), extending up to a distance of 500 nautical miles, represented by the label "500 NM."
---
### Question Options:
Below the diagram, there are several options provided to choose from, which represent the components of the vector in terms of trigonometric functions:
1. **Option 1**:
\[
(500 \cdot \tan(36°), 500 \cdot \tan(54°))
\]
2. **Option 2**:
\[
(500 \cdot \cos(36°), 500 \cdot \sin(36°))
\]
3. **Option 3**:
\[
(500 \cdot \cos(54°), 500 \cdot \sin(54°))
\]
4. **Option 4**:
\[
(500 \cdot \sin(36°), 500 \cdot \cos(36°))
\]
5. **Option 5**:
\[
(500 \cdot \sin(54°), 500 \cdot \cos(54°))
\]
---
### Navigation Instructions:
There are navigation buttons at the bottom of the page numbered from 7 to 16, allowing users to move through the educational content. There are also additional navigation and interaction tools on a vertical toolbar to the right side of the interface including options to go back, flag, or use a calculator.
---
### Note:
To solve this problem, one must decompose the vector into its North and East components using sine and cosine functions for the given angle (38°).
---
**End of Educational Content**
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (11th Edition)
Trigonometry
ISBN:
9780134217437
Author:
Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:
PEARSON
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning