Which of the following is the direction angle of v = (-3,- ? Round your answer to the nearest hundredth of a degree. 140.19° 320.19° 39.19° 219.81°
Which of the following is the direction angle of v = (-3,- ? Round your answer to the nearest hundredth of a degree. 140.19° 320.19° 39.19° 219.81°
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.1: Angles
Problem 2E
Related questions
Question
![**Vector Direction Angle Problem**
**Problem Statement:**
Determine the direction angle of vector **v** = ⟨ -√3, 3/2 ⟩. Round your answer to the nearest hundredth of a degree.
**Options:**
- 140.19°
- 320.19°
- 39.19°
- 219.81°
**Explanation:**
To find the direction angle of a vector, use the following formula:
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]
Where:
- \( x \) and \( y \) are the components of the vector.
- \( \theta \) is the direction angle.
In this case, the vector is **v** = ⟨ -√3, 3/2 ⟩.
Let's apply the formula:
\[
\theta = \tan^{-1}\left(\frac{3/2}{-√3}\right)
\]
Make sure to consider the sign of the components and the quadrant in which the vector lies for the correct angle.
**Multiple-choice options are provided for your answer.**
Note: The answer needs to be rounded to the nearest hundredth of a degree.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc5bcc65-7283-4529-b9b7-ffbb90a5afc1%2Fee5e1e5c-5af6-4994-acd2-8a938e794b17%2F06xaaw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Vector Direction Angle Problem**
**Problem Statement:**
Determine the direction angle of vector **v** = ⟨ -√3, 3/2 ⟩. Round your answer to the nearest hundredth of a degree.
**Options:**
- 140.19°
- 320.19°
- 39.19°
- 219.81°
**Explanation:**
To find the direction angle of a vector, use the following formula:
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]
Where:
- \( x \) and \( y \) are the components of the vector.
- \( \theta \) is the direction angle.
In this case, the vector is **v** = ⟨ -√3, 3/2 ⟩.
Let's apply the formula:
\[
\theta = \tan^{-1}\left(\frac{3/2}{-√3}\right)
\]
Make sure to consider the sign of the components and the quadrant in which the vector lies for the correct angle.
**Multiple-choice options are provided for your answer.**
Note: The answer needs to be rounded to the nearest hundredth of a degree.
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