Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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![**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**](https://content.bartleby.com/qna-images/question/26056068-ea34-4e16-9a12-19cfd54f09f4/956a1262-868c-4357-9842-32a109d70ed3/mu6uoi9_processed.png)
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**
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