4. Find the magnitude and direction angle (to the nearest tenth) of the vector (-7,24). Sketch a picture and make sure your angle is in the correct quadrant!
4. Find the magnitude and direction angle (to the nearest tenth) of the vector (-7,24). Sketch a picture and make sure your angle is in the correct quadrant!
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°.
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![**Problem 4: Vector Magnitude and Direction**
**Task:**
Find the magnitude and direction angle (to the nearest tenth) of the vector \(\langle -7, 24 \rangle\).
**Instructions:**
1. Calculate the magnitude of the vector.
2. Determine the direction angle, ensuring it is in the correct quadrant.
3. Sketch a diagram of the vector to visualize its position.
**Notes:**
- The magnitude of a vector \(\langle x, y \rangle\) is calculated using the formula:
\[
\text{Magnitude} = \sqrt{x^2 + y^2}
\]
- The direction angle \(\theta\) can be found using:
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]
Adjust the angle based on the quadrant where the vector lies.
- Ensure the angle is in degrees (not radians) and round to the nearest tenth.
**Quadrant Check:**
Given the components \(-7\) and \(24\), the vector lies in the second quadrant. Adjust the angle calculation accordingly.
**Visualization:**
Sketch the vector on a Cartesian plane to confirm its position and angle visually.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F681a1dd5-ea79-4df0-af09-f7e014c18f3f%2F7f74f9c1-3632-432b-a1a2-349042ec3539%2Fvx5r4lr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 4: Vector Magnitude and Direction**
**Task:**
Find the magnitude and direction angle (to the nearest tenth) of the vector \(\langle -7, 24 \rangle\).
**Instructions:**
1. Calculate the magnitude of the vector.
2. Determine the direction angle, ensuring it is in the correct quadrant.
3. Sketch a diagram of the vector to visualize its position.
**Notes:**
- The magnitude of a vector \(\langle x, y \rangle\) is calculated using the formula:
\[
\text{Magnitude} = \sqrt{x^2 + y^2}
\]
- The direction angle \(\theta\) can be found using:
\[
\theta = \tan^{-1}\left(\frac{y}{x}\right)
\]
Adjust the angle based on the quadrant where the vector lies.
- Ensure the angle is in degrees (not radians) and round to the nearest tenth.
**Quadrant Check:**
Given the components \(-7\) and \(24\), the vector lies in the second quadrant. Adjust the angle calculation accordingly.
**Visualization:**
Sketch the vector on a Cartesian plane to confirm its position and angle visually.
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